World!Of Numbers |
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[ May 1, 2022 ] Both sum and product of the prime factors (without multiplicity) are palindromic.
There are 8 solutions for the pandigitals and only one for the ninedigitals.
Here is some Pari/gp code to reproduce Alexandru's results. { for(n=1,10!, d=numtoperm(10, n+10!-1); a=sum(i=1, #d, (d[i]-1)*10^(#d-i)); f=factor(a); sf=0; mf=1; for(j=1,#f~, sf+=f[j,1]; mf*=f[j,1]); dsf=digits(sf); dmf=digits(mf); if(Vecrev(dsf)==dsf && Vecrev(dmf)==dmf, print(a," ",f," sum = ",sf,", product = ",mf)); ); } The pandigital 4357812096 (#7) appears also in wonplate 26. It is the product of these two palindromes : 69696 * 62526 = 4357812096 | |||||||||||||||||||||||||||||||||||||||||||||||||||
A000217 Prime Curios! Prime Puzzle Wikipedia 217 Le nombre 217 |
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