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A335761 Nonnegative numbers that are the difference between a positive tetrahedral number and a positive cubic number.

%I A335761 #31 Jan 09 2021 02:08:46
%S A335761 0,2,3,4,8,9,12,19,20,21,27,29,34,40,43,47,48,53,55,56,57,70,76,83,87,
%T A335761 93,95,101,103,112,119,136,138,140,144,148,152,156,157,161,164,168,
%U A335761 174,181,193,209,212,217,219,222,239,240,253,259,275,278,279,281,285
%N A335761 Nonnegative numbers that are the difference between a positive tetrahedral number and a positive cubic number.
%C A335761 The sequence is the difference between the tetrahedral number (A000292) and the cubic number (A000578) such that terms are of the form A000292(i)-A000578(j), where A000292(i) >= A000578(j) >= 0.
%C A335761 It appears that sequence terms are more scarce than prime numbers. The number of terms in this sequence (n) and the number of prime numbers up to a(n) are shown in the figure attached in the LINKS section. It can be seen that, for a(n) > 304, n is less than pi(a(n)), where pi is the prime counting function.
%H A335761 Ya-Ping Lu, <a href="/A335761/a335761_1.pdf">The number of terms in a(n) and the number of prime numbers up to a(n)</a>
%F A335761 The difference between the i-th tetrahedral number, t(i), and j-th cubic number, c(j) is d = i*(i+1)*(i+2)/6 - j^3, where i, j >=1 and t(i) >= c(j).
%e A335761 a(1)=0 because t(1)-c(1)=1-1=0;
%e A335761 a(2)=2 because t(3)-c(2)=10-8=2;
%e A335761 a(7)=12 because t(4)-c(2)=20-8=12, and t(39)-c(22)=10660-10648=12;
%e A335761 a(19)=55 because t(6)-c(1)=56-1=55, and t(4669)-c(2570)=16974593055-16974593000=55.
%Y A335761 Cf. A000292, A000578, A230044, A328792.
%K A335761 nonn
%O A335761 1,2
%A A335761 _Ya-Ping Lu_, Jun 21 2020