A137996 -id:A137996 - cp's OEIS frontend

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

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M. F. Hasler, Mar 24 2008

nonn

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).

Zhi-Wei SUN, A new conjecture: n=p+x(x+1)/2, Mar 23, 2008.

Cf. A137996, A132399, A000040, A000217.

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"," ))

cp's OEIS Frontend

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

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