cp's OEIS Frontend

A076768 Positive integers not expressible as the sum of a prime and a triangular number.

%I A076768 #27 Jul 30 2019 16:55:23
%S A076768 1,36,105,171,210,216,325,351,406,528,561,630,741,780,990,1081,1176,
%T A076768 1275,1596,1711,1830,1953,2016,2145,2346,2628,2775,3003,3081,3240,
%U A076768 3321,3655,3741,3916,4278,4371,4465,4560,4851,5253,5460,5565,5886,6105,6216,6786,7021,7140,7503,7626,7750,7875,8256,8515,8911,9045,9591,9870
%N A076768 Positive integers not expressible as the sum of a prime and a triangular number.
%C A076768 It appears that 1,2,3,8 are the only positive integers that cannot be partitioned as the sum of a semiprime and a triangular number. Here triangular numbers include t(0)=0 and t(1)=1. - _Jonathan Vos Post_ and _Ray Chandler_, Nov 28 2004
%C A076768 This sequence contains 216 (and possibly other nontriangular numbers) together with an infinite number of triangular numbers. The indices of the triangular numbers are in A138666. This is related to the Sun's conjecture (see A132399) that every number except 216 is the sum of a triangular number and a prime or 0. - _T. D. Noe_, Mar 26 2008
%H A076768 T. D. Noe, <a href="/A076768/b076768.txt">Table of n, a(n) for n=1..1001</a>
%e A076768 a(2) = 36 is an element of this sequence because 36 cannot be written as a sum of one of the primes <= 36 {2,3,5,7,11,13,17,19,23,29,31} and one of the triangular numbers <= 36 {1,3,6,10,15,21,28,36}. - corrected (added 28) by _Gionata Neri_, May 02 2015
%t A076768 Complement[Range[9871],Total/@Tuples[{Prime[Range[1220]],Accumulate[ Range[ 0,140]]}]] (* _Harvey P. Dale_, Jul 30 2019 *)
%Y A076768 Cf. A000040, A000217, A046903.
%K A076768 nonn
%O A076768 1,2
%A A076768 _Jason Earls_, Nov 14 2002
%E A076768 Added the terms 6786 through 9870 and conjecture that there are no further terms - _Jonathan Vos Post_ and _Ray Chandler_, Nov 28 2004
%E A076768 Added "positive" to the name - _Alex Ratushnyak_, Apr 04 2013