\(300\mathbf{\color{blue}{\;=\;}}\) als som van opeenvolgende gehele getallen op drie verschillende wijzen :

\begin{cases} 301=15,16,17,18,19,20,21,22,23,24,25,26,27,28\\ 301=40,41,42,43,44,45,46\\ 301=150+151 \end{cases}

\(301\mathbf{\color{blue}{\;=\;}}37+39+41+43+45+47+49\) (som van opeenvolgende onpare getallen)

\(301\mathbf{\color{blue}{\;=\;}}97+101+103\) (som van opeenvolgende priemgetallen)

\(301\mathbf{\color{blue}{\;=\;}}((0;3;6;16)\,(0;6;11;12)\,(1;2;10;14)\,(1;10;10;10)\,(2;2;2;17)\,(2;3;12;12)\,(2;4;5;16)\)

\(\qquad~~~~(2;6;6;15)\,(2;8;8;13)\,(4;4;10;13)\,(4;5;8;14)\,(4;8;10;11))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#12\}\)

\(301\mathbf{\color{blue}{\;=\;}}((0;0;0;2;2;2;3;5;5)\,(0;1;1;1;1;3;3;3;6)\,(0;1;3;3;3;3;4;4;4)\,(1;1;1;1;1;2;2;4;6)\)

\(\qquad~~~~(1;1;2;2;3;4;4;4;4)\,(2;2;2;2;2;2;4;4;5))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#6\}\)

\(301\mathbf{\color{blue}{\;=\;}}2^2+2^3+17^2\)

\(301\mathbf{\color{blue}{\;=\;}}43*(4+3)\)

\(301\mathbf{\color{blue}{\;=\;}}[5^4][25^2]-18^2\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{151^2-150^2}\mathbf{\color{blue}{\;=\;}}401^3-8030^2\)

301.1

\(301\mathbf{\color{blue}{\;=\;}}\)(som van drie derdemachten)

\(\qquad~~~~\)References Sum of Three Cubes

\(\qquad~~~~\)Getallen van de vorm \(~9m+4~\) of \(~9m+5~\) kunnen nooit als som van drie derdemachten geschreven worden.

\(\qquad~~~~\)In dit geval is \(m=33~~(+4)\).

\(301\mathbf{\color{blue}{\;=\;}}\)(som van vier derdemachten)

\(\qquad~~~~(z\gt1000)\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-11)^3+(-14)^3+(-26)^3+28^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-2)^3+(-26)^3+(-32)^3+37^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-23)^3+(-23)^3+(-38)^3+43^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{22^3+37^3+40^3+(-50)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{1^3+34^3+55^3+(-59)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{10^3+22^3+61^3+(-62)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-5)^3+(-38)^3+(-95)^3+97^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-26)^3+61^3+130^3+(-134)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-47)^3+(-71)^3+(-173)^3+178^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{37^3+(-62)^3+(-176)^3+178^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{28^3+(-122)^3+(-179)^3+196^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{43^3+(-68)^3+(-197)^3+199^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{40^3+139^3+193^3+(-215)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-23)^3+55^3+226^3+(-227)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-62)^3+97^3+235^3+(-239)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-23)^3+193^3+196^3+(-245)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{91^3+142^3+223^3+(-245)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{139^3+(-179)^3+(-236)^3+253^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-155)^3+226^3+235^3+(-275)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{40^3+(-83)^3+(-290)^3+292^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{16^3+(-194)^3+(-275)^3+304^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{10^3+(-131)^3+(-302)^3+310^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{1^3+106^3+313^3+(-317)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{136^3+208^3+277^3+(-320)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{133^3+211^3+280^3+(-323)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{193^3+(-236)^3+(-305)^3+325^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{109^3+154^3+313^3+(-329)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{199^3+(-236)^3+(-347)^3+361^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-74)^3+148^3+364^3+(-371)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{31^3+73^3+373^3+(-374)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{169^3+(-197)^3+(-431)^3+436^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{172^3+307^3+367^3+(-437)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-191)^3+(-227)^3+(-404)^3+439^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{202^3+274^3+418^3+(-467)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{280^3+(-320)^3+(-452)^3+469^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-299)^3+412^3+442^3+(-506)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-308)^3+412^3+469^3+(-524)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{61^3+217^3+511^3+(-524)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{25^3+(-221)^3+(-566)^3+577^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{58^3+157^3+580^3+(-584)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-179)^3+214^3+580^3+(-584)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{148^3+(-452)^3+(-491)^3+592^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{196^3+(-467)^3+(-497)^3+601^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-95)^3+367^3+592^3+(-635)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{49^3+478^3+553^3+(-653)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{52^3+(-188)^3+(-656)^3+661^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{88^3+(-248)^3+(-659)^3+670^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{1^3+325^3+664^3+(-689)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{190^3+253^3+685^3+(-701)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{277^3+(-464)^3+(-656)^3+712^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-23)^3+(-329)^3+(-707)^3+730^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{214^3+(-491)^3+(-662)^3+736^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-107)^3+(-230)^3+(-743)^3+751^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{277^3+(-326)^3+(-743)^3+751^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{340^3+(-515)^3+(-692)^3+754^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-56)^3+(-149)^3+(-761)^3+763^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{94^3+436^3+730^3+(-779)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{445^3+460^3+664^3+(-782)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{565^3+(-620)^3+(-761)^3+793^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{118^3+562^3+685^3+(-794)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{256^3+475^3+733^3+(-803)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-200)^3+(-608)^3+(-683)^3+820^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{277^3+(-440)^3+(-800)^3+832^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{205^3+(-269)^3+(-848)^3+853^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{643^3+(-785)^3+(-797)^3+898^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-98)^3+649^3+793^3+(-917)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-53)^3+139^3+919^3+(-920)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-353)^3+412^3+925^3+(-935)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-701)^3+799^3+874^3+(-941)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{349^3+508^3+874^3+(-944)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{583^3+(-620)^3+(-971)^3+985^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-5)^3+(-317)^3+(-977)^3+988^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{613^3+664^3+778^3+(-998)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{589^3+(-842)^3+(-896)^3+1036^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{421^3+(-683)^3+(-989)^3+1066^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-155)^3+(-800)^3+(-899)^3+1075^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-452)^3+781^3+982^3+(-1100)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{175^3+784^3+949^3+(-1103)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{229^3+(-824)^3+(-929)^3+1105^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-605)^3+(-872)^3+(-917)^3+1183^3}\mathbf{\color{blue}{\;=\;}}\)

\(301\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

\(\qquad~~~~\)(fully searched up to \(z=1000)\)

\(\qquad~~~~\bbox[lightyellow,3px,border:1px blue solid]{~oplossing~onbekend~}\mathbf{\color{blue}{\;=\;}}\)

301.2

\(301^2\mathbf{\color{blue}{\;=\;}}949^2-[30^4][900^2]\mathbf{\color{blue}{\;=\;}}1030^2-99^3\mathbf{\color{blue}{\;=\;}}1075^2-1032^2\mathbf{\color{blue}{\;=\;}}6475^2-6468^2\)

\(301^3\mathbf{\color{blue}{\;=\;}}7525^2-5418^2\mathbf{\color{blue}{\;=\;}}8299^2-6450^2\mathbf{\color{blue}{\;=\;}}\cdots\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{45451^2-45150^2}\)

301.3
\(301^2=250^2+275^2-218^2\) 301.4
  EEN PUZZEL  

\(\bbox[3px,border:1px solid blue]{\;Opgave\;}\)
Het volgende raadsel is een klassieker. Iemand heeft een verzameling munten. Als hij de munten per \(2\), per \(3\), per \(4\),
per \(5\) of per \(6\) legt, blijft er telkens één munt over. In rijen van \(7\) gelegd, blijft er geen enkele over. Hoeveel munten
heeft de man minimaal ?
\(\bbox[3px,border:1px solid blue]{\;Oplossing\;}\)
Het kleinste gemeen veelvoud van \(2,3,4,5,6\) is \(60\). We vertrekken daarom van \(60\), met \(1\) vermeerderd. Maar het
aantal kan natuurlijk ook een veelvoud van \(60\) zijn, vermeerderd met \(1\). We moeten nu een veelvoud van \(7\) zoeken
dat overeenkomt met een veelvoud van \(60\), plus \(1\). We berekenen achtereenvolgens \(60*k+1\) voor \(k=1,2,3,4,\ldots\)
en bepalen tegelijk wanneer de deling \((60*k+1)/7\) opgaat :

k\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)
\(60*k+1\)\(61\)\(121\)\(181\)\(241\)\(301\)\(361\)
\(/~door~7\)\(8,714\)\(17,286\)\(25,857\)\(34,429\)\(43\)\(51,571\)

De deling gaat op voor \(6*k+1=301\). Er zijn dus minimaal \(301\) muntstukken. Grotere aantallen zijn ook mogelijk,
bvb. \(721,1141,\ldots\) d.w.z. \(301\) + een veelvoud van \(420\) (\(420\) is het kleinste gemeen veelvoud van \(2,3,4,5,6~\) en \(~7\,\)).
Men vindt deze aantallen door de volgende formule toe te passen :
\(1+300+420*n=1+5*60+7*n*60\) wat we kunnen schrijven als \(((5+n*7)*60)+1\).
Het geval \(n=0\) levert het minimale aantal op. Voor \(n=1\) vindt men \(721\); voor \(n=2\) krijgt men \(1141\), enz.

Zie ook

301.5

De eerste keer dat er \(301\) opeenvolgende samengestelde getallen voorkomen gebeurt tussen de priemgetallen
\(6675573497~\) en \(~6675573799\) met aldus een priemkloof van \(302\,.~~\) (OEIS A000101.pdf)

301.6
Men moet \(301\) tot minimaal de \(103593\)ste macht verheffen opdat in de decimale expansie exact \(301\) \(301\)'s verschijnen.
Terloops : \(301\)\(^{103593}\) heeft een lengte van \(256763\) cijfers.
301.7

\(\begin{aligned}301\mathbf{\color{blue}{\;=\;}}\left({\frac{382}{57}}\right)^3+\left({\frac{5}{57}}\right)^3\end{aligned}\)

(Integral Sum of Two Rational Cubes) (OEIS A020898) (OEIS A228499) (Links uit OEIS A060838)

\((x^3+y^3)/z^3=n~\to~\) [x waarde] (OEIS A190356)  [y waarde] (OEIS A190580)  [z waarde] (OEIS A190581)

Kleinste positieve oplossingen \(~\to~\) [x waarde] (OEIS A254326)  [y waarde] (OEIS A254324)

301.8

\(b\mathbf{\color{blue}{\;=\;}}301\to\)
\(b\)\(^{2}\)\(+b\)\(^{0}\)\(+b\)\(^{4}\)\(+b\)\(^{1}\)\(+b\)\(^{6}\)\(+b\)\(^{1}\)\(+b\)\(^{8}\)\(+b\)\(^{6}\)\(+b\)\(^{5}\)\(+b\)\(^{3}\)\(+b\)\(^{5}\)\(+b\)\(^{3}\)\(+b\)\(^{4}\)\(+b\)\(^{1}\)\(+b\)\(^{0}\)\(+b\)\(^{3}\)\(+b\)\(^{0}\)\(+b\)\(^{5}\)\(+b\)\(^{8}\)\(+b\)\(^{4}\)\(+b\)\(^{9}\)\(+b\)\(^{2}\)\(+b\)\(^{3}\)\(\mathbf{\color{blue}{\;=\;}}\)
\(20416186535341030584923~~\) (OEIS A236067)

301.9
Het kleinste getal dat exact \(301\) delers heeft is \(3206175906594816=2^{42}*3^6\) (OEIS A005179) 301.10

 ○–○–○ 

\(301^2=90601~~\) en \(~~906/(prime(prime(0!)))-1=301\)
\(301^3=27270901~~\) en \(~~?=301\)
\(301^4=8208541201~~\) en \(~~?=301\)
\(301^5=2470770901501~~\) en \(~~?=301\)
\(301^6=743702041351801~~\) en \(~~?=301\)
\(301^7=223854314446892101~~\) en \(~~?=301\)
\(301^8=67380148648514522401~~\) en \(~~?=301\)
\(301^9=20281424743202871242701~~\) en \(~~?=301\) 		301.11

Som Der Cijfers (\(sdc\)) van \(k^{\large{301}}\) is gelijk aan het grondtal \(k\). De triviale oplossingen \(0\) en \(1\) negerend vinden we :

\(\qquad\qquad~sdc\left(4959^{\large{301}}\right)=4959\qquad\qquad~sdc\left(4968^{\large{301}}\right)=4968\qquad\qquad~sdc\left(4973^{\large{301}}\right)=4973\)

\(\qquad\qquad~sdc\left(5035^{\large{301}}\right)=5035\qquad\qquad~sdc\left(5042^{\large{301}}\right)=5042\qquad\qquad~sdc\left(5065^{\large{301}}\right)=5065\)

\(\qquad\qquad~sdc\left(5075^{\large{301}}\right)=5075\qquad\qquad~sdc\left(5116^{\large{301}}\right)=5116\)

301.12

Expressie met tweemaal de cijfers uit het getal \(301\) enkel met operatoren \(+,-,*,/,(),\)^^\(\)
\(301\mathbf{\color{blue}{\;=\;}}3\)^^\(0\)^^\(0+3-1-1\)

301.13

Als expressie met enkelcijferige toepassing, resp. van \(1\) tot \(9~~\) (met o.a. dank aan Inder. J. Taneja).
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}(1+1+1)*(11-1)^{(1+1)}+1\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}((22+2)^2+22)/2+2\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}3*3*33+3+3/3\mathbf{\color{blue}{\;=\;}}333-33+3/3\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}4^4+44+4/4\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}5*(55+5)+5/5\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}(66-6)*(6-6/6)+6/6\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}7*(7*7-7)+7\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}(8+8)*(8+8)+8*8-8-88/8\)
\(\qquad\qquad301\mathbf{\color{blue}{\;=\;}}(9+99/9)^{((9+9)/9)}-99\)

301.14

Met de cijfers van \(1\) tot \(9\) in stijgende en dalende volgorde (met dank aan Inder. J. Taneja) :
\(\qquad\qquad301=1+2*3*45+6+7+8+9\)
\(\qquad\qquad301=9+8+7+6+54*(3+2)+1\)

301.15
The number \(301*2^{184}+1\) is the second smallest Proth prime with \(k=301\to\) (\(301*2^{4}+1\) is the smallest).
(OEIS A322915) 		301.16
\(301\) is het aantal snijpunten van diagonalen binnen een regelmatige twaalfhoek.
(OEIS A006561) 		301.17
\(301^2=90601~~\) en \(~~103^2=10609\). 301.18
  WETENSWAARD  

\(301\) is één van de zes getallen die, wanneer ze in het kwadraat gezet worden, dezelfde cijfers gebruiken.
\(103^2=10609~~;~~130^2=16900~~;~~140^2=19600~~;~~247^2=61009~~;~~301^2=90601~~\) en \(~~310^2=96100\)

301.19
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

⏮

⯬

⏴

⏵

⯮

⏭

\(301\)\(7*43\)\(4\)\(352\)
\(1,7,43,301\)
\(100101101_2\)\(455_8\)\(12\)D\(_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 17 januari 2026