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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 (list; graph; refs; listen; history; text; internal format)
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 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.

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, 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

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Last modified August 7 09:09 EDT 2020. Contains 336274 sequences. (Running on oeis4.)