

A114913


Numbers n such that A114912(n)=1. Numbers n such that A000009(n) == 2 (mod 4).


3



3, 4, 8, 10, 13, 14, 17, 18, 19, 24, 25, 28, 32, 39, 42, 43, 47, 48, 50, 52, 54, 55, 62, 67, 69, 73, 74, 75, 76, 78, 83, 84, 87, 88, 89, 90, 95, 99, 101, 103, 105, 108, 109, 112, 113, 118, 119, 123, 125, 127, 130, 132, 134, 138, 140, 143, 144, 147, 149, 153, 154, 157
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OFFSET

1,1


COMMENTS

All terms are the sum of a generalized pentagonal number A001318 and a square A000290.
Let 24*n+1 = p_1^e_1 * ... * p_r^e_r * q_1^f_1 * ... * q_s^f_s, where the p_i's are distinct primes == 1, 5, 7, or 11 (mod 24) and the q_i's are distinct primes == 13, 17, 19, or 23 (mod 24). Then n belongs to the sequence iff all of the f_i's are even and all but one of the e_i's are even and the one e_i which is odd is == 1 (mod 4). (Dean Hickerson, Jan 19 2006)
All values are the sum of a generalized pentagonal number A001318 and a square A000290.


LINKS

Table of n, a(n) for n=1..62.
K. Alladi, Partition Identities Involving Gaps and Weights, Transactions of the American Mathematical Society, Vol. 349, No. 12, Dec 1997, pp. 50015019.


CROSSREFS

Cf. A114914.
A111174 is a subsequence. See comments in A113780 for explanation.
Sequence in context: A083317 A268514 A024514 * A111174 A075751 A065153
Adjacent sequences: A114910 A114911 A114912 * A114914 A114915 A114916


KEYWORD

nonn


AUTHOR

Christian G. Bower, Jan 06 2006


STATUS

approved



