A262044 -id:A262044 - cp's OEIS frontend

A058848 Numbers k such that the sum of the first k odd composites is palindromic.

1, 12, 25, 61, 108, 211, 1344, 2339, 10539, 78409, 283181, 1748747, 1795423, 2386702, 2819089, 179101605, 1923088106, 2822581688, 7794689270, 17381011919, 25635268093, 28780043265, 97973526253

Offset: 1

Patrick De Geest, Dec 15 2000

Sequence of odd composite numbers is 9 + 15 + 21 + 25 + 27 + 33 + ... + z. For values of z see A058849.

Patrick De Geest, Palindromic Sums

Cf. A058849, A058850, A262044.

Position[Accumulate[Select[Range[9,10^7,2],CompositeQ]],?(PalindromeQ[#]&)]//Flatten (* The program generates the first 15 terms of the sequence. *) (* _Harvey P. Dale, Aug 05 2025 *)

a(20) from Donovan Johnson, Sep 01 2012
a(21)-a(23) from Chai Wah Wu, Dec 06 2019
Comment clarified by Harvey P. Dale, Aug 05 2025

A383641 a(n) is the difference between the sum of even composites and the sum of the odd composites in the first n positive integers.

Original entry on oeis.org

0, 0, 0, 4, 4, 10, 10, 18, 9, 19, 19, 31, 31, 45, 30, 46, 46, 64, 64, 84, 63, 85, 85, 109, 84, 110, 83, 111, 111, 141, 141, 173, 140, 174, 139, 175, 175, 213, 174, 214, 214, 256, 256, 300, 255, 301, 301, 349, 300, 350, 299, 351, 351, 405, 350, 406, 349, 407, 407

Offset: 1

Felix Huber, May 08 2025

nonn

			Of the first 9 positive integers, 4, 6, and 8 are even composites and 9 is an odd composite, so a(9) = 4 + 6 + 8 - 9 = 9.

Felix Huber, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Composite Number

Cf. A000720, A002808, A004526, A010701, A028552, A034387, A066247, A071904, A101256, A193356, A262044, A383259.

A383641:=n->`if`(n=1,0,floor((n-2)/2)-n*(n mod 2)+add(ithprime(i),i=2..NumberTheory:-pi(n)));seq(A383641(n),n=1..59);

lim=59;cn=Select[Range[lim],CompositeQ];a[n_]:=Total[Select[cn,EvenQ[#]&&#<=n&]]-Total[Select[cn,OddQ[#]&&#<=n&]];Array[a,lim] (* James C. McMahon, May 14 2025 *)

a(n) = floor((n-2)/2) - n*(n mod 2) + Sum_{i=2..pi(n)} prime(i) for n > 1.
a(n) = A004526(n) - A193356(n) - A010701(n) + A034387(A000720(n)) for n > 1.
a(n) = Sum_{i=1..n} ((-1)^i*i*A066247(i)).

cp's OEIS Frontend

A058848 Numbers k such that the sum of the first k odd composites is palindromic.

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