

A137997


Numbers which are not the sum of a triangular number and zero or a prime = 3 (mod 4).


2



2, 5, 16, 27, 30, 42, 54, 61, 63, 90, 96, 129, 144, 165, 204, 216, 225, 285, 288, 309, 333, 340, 345, 390, 405, 423, 426, 448, 462, 525, 540, 556, 624, 651, 705, 801, 813, 876, 945, 960, 1056, 1230, 1371, 1380, 1470, 1491, 1827, 2085, 2157, 2181, 2220, 2355
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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 A137997(1..112) = 2,...,90441 are the only numbers which cannot be written in this form with p=0 or p=3 (mod 4).


LINKS

Table of n, a(n) for n=1..52.
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, p = t++ ); until( !t, isprime( p+=t )  next; p%4==3 && next(2)); print1( n", " ))


CROSSREFS

Cf. A137996, A132399, A000040, A000217.
Sequence in context: A175735 A275172 A281980 * A213359 A328000 A323006
Adjacent sequences: A137994 A137995 A137996 * A137998 A137999 A138000


KEYWORD

nonn


AUTHOR

M. F. Hasler, Mar 24 2008


STATUS

approved



