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Pa!indromic Sums of the first n 'type of numbers'
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1. Sum of the first n primes is palindromic
2. Sum of the first n odd primes is palindromic
3. Sum of the first n composites is palindromic
4. Sum of the first n odd composites is palindromic
5. Sum of the first n even composites is palindromic
6. Sum of the first n palindromes is palindromic
7. Sum of the first n numbers is palindromic
8. Sum of the first n odd numbers is palindromic
9. Sum of the first n even numbers is palindromic

1. Sum of the first n primes is palindromic.

Sequence = 2 + 3 + 5 + 7 + 11 + 13 + ... + z
Index entries in OEIS A038582, A038584 and A038583
Other sources : Puzzle 7

2. Sum of the first n odd primes is palindromic.

Sequence = 3 + 5 + 7 + 11 + 13 + 17 + ... + z
Index entries in OEIS A058845, A058846 and A058847

3. Sum of the first n composites is palindromic.

Sequence = 4 + 6 + 8 + 9 + 10 + 12 + ... + z
Index entries in OEIS A053779, A057959 and A053780
Other sources : Puzzle 89

4. Sum of the first n odd composites is palindromic.

Sequence = 9 + 15 + 21 + 25 + 27 + 33 + ... + z
Index entries in OEIS A058848, A058849 and A058850
Other sources : Puzzle 89

5. Sum of the first n even composites is palindromic.

Sequence = 4 + 6 + 8 + 10 + 12 + 14 + ... + z
Index entries in OEIS A028553, A058851 and A028554

Aldo Palindromic numbers of the form n(n+3).
Main source see Palindromes of the form n(n+3)

The following substitution shows why the sequence equals x * (x + 3)

The sequence can be rewritten as 2 * (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...)
The second term is 'the sum of the natural numbers' minus the starting number 1.
Replace it with the general formula we get 2 * [ (n^2 + n)/2 – 1 ] or [ n^2 + n – 2 ]
Substitute n with (x + 1) we get [ (x + 1)^2 + (x + 1) – 2 ] and work it out.
The sequence evolves from [ x^2 + 2x + 1 + x + 1 – 2 ] to [ x^2 + 3x ]
which finally yields to x * (x + 3) QED

Index	n	z	palindromic sum
1	1	4	4
2	8	18	88
3	28	58	868
4	66	134	4554
5	88	178	8008
6	211	424	45154
7	298	598	89698
8	671	1344	452254
9	2126	4254	4526254
10	2998	5998	8996998
11	28814	57630	830333038
12	29369	58740	862626268
13	29998	59998	899969998
14	63701	127404	4058008504
15	212206	424414	45032023054
16	212671	425344	45229592254
17	299998	599998	89999699998
18	636776	1273554	405485584504
19	2122206	4244414	4503764673054
20	2861419	5722840	8187727277818
21	2999998	5999998	8999996999998
22	9443423	18886848	89178266287198
23	21341691	42683384	455467838764554
24	28862883	57725768	833066101660338
25	29999998	59999998	899999969999998
26	212325206	424650414	45081993739918054
27	289053683	578107368	83552032523025538
28	294127328	588254658	86510885958801568
29	294174669	588349340	86538736763783568
30	299999998	599999998	89999999699999998 = Infinite pattern
Continued at Palindromes of the form n(n+3)

6. Sum of the first n palindromes is palindromic.

Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z
Index entries in OEIS A046486 and A046487

7. Sum of the first n numbers is palindromic.

Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z
Main source see Palindromic Triangulars

8. Sum of the first n odd numbers is palindromic.

Sequence = 1 + 3 + 5 + 7 + 9 + 11 + ... + z
Main source see Palindromic Squares

9. Sum of the first n even numbers is palindromic.

Sequence = 2 + 4 + 6 + 8 + 10 + 12 + ... + z
Main source see Palindromic Pronic Numbers

Enoch Haga (email) from California, USA.

Jeff Heleen (email) from New Hampshire, USA.

G. L. Honaker, Jr. (email) from Bristol, Virginia, USA.

Jud McCranie (email) from USA.

Carlos Rivera (email) from Monterrey, Nuevo León, México.

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