A137997 Numbers which are not the sum of a triangular number and zero or a prime = 3 (mod 4).

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

Offset

1,1

Comments

Zhi-Wei 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.

Zhi-Wei 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 = n-t*(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