

A137996


Numbers which are not the sum of a triangular number and zero or a prime = 1 (mod 4).


2



2, 4, 7, 9, 12, 22, 24, 25, 31, 46, 48, 70, 75, 80, 85, 87, 93, 121, 126, 135, 148, 162, 169, 186, 205, 211, 213, 216, 220, 222, 246, 255, 315, 331, 357, 375, 396, 420, 432, 441, 468, 573, 588, 615, 690, 717, 735, 738, 750, 796, 879, 924, 1029, 1038, 1080, 1155
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OFFSET

1,1


COMMENTS

ZhiWei SUN conjectured that n=216 is the only number not of the form n = p + k(k+1)/2 with p a prime or zero and more precisely that the numbers given in this sequence A137996(1..123) = 2,...,88956 are the only numbers which cannot be written in this form with p=0 or p=1 (mod 4).


LINKS

Table of n, a(n) for n=1..56.
ZhiWei SUN, A new conjecture: n=p+x(x+1)/2, Mar 23, 2008.


PROG

(PARI) { for( n=1, 10^8, t=sqrtint(2*n); if( 0 >= p =nt*(t+1)/2, !p & next, isprime(p) & p%4==1 & next); until( !t, isprime( p+=t ) & p%4==1 & next(2)); print1(n", "))}


CROSSREFS

Cf. A137997, A132399, A000040, A000217.
Sequence in context: A212988 A064491 A120878 * A080057 A087158 A195669
Adjacent sequences: A137993 A137994 A137995 * A137997 A137998 A137999


KEYWORD

nonn


AUTHOR

M. F. Hasler, Mar 24 2008


STATUS

approved



