cp's OEIS Frontend

A298462 The first of two consecutive triangular numbers the sum of which is equal to the sum of two consecutive prime numbers.

%I A298462 #10 Jan 20 2018 02:41:39
%S A298462 15,45,66,276,861,1128,1891,2556,3486,4005,5995,7140,7381,15051,20706,
%T A298462 21528,24090,26796,28680,34716,46665,52975,56280,69006,74305,83028,
%U A298462 83845,98346,102831,103740,109278,110215,112101,135981,148785,150975,176121,179700
%N A298462 The first of two consecutive triangular numbers the sum of which is equal to the sum of two consecutive prime numbers.
%H A298462 Robert Israel, <a href="/A298462/b298462.txt">Table of n, a(n) for n = 1..10000</a>
%e A298462 45 is in the sequence because 45+55 (consecutive triangular numbers) = 100 = 47+53 (consecutive primes).
%p A298462 f:= proc(n) local p,q;
%p A298462   p:= prevprime(floor((n+1)^2/2)); q:= nextprime(p);
%p A298462   if p+q = (n+1)^2 then n*(n+1)/2 else NULL fi
%p A298462 end proc:
%p A298462 map(f, [$2..1000]); # _Robert Israel_, Jan 19 2018
%o A298462 (PARI) L=List(); forprime(p=2, 200000, q=nextprime(p+1); t=p+q; if(issquare(4*t, &sq) && (sq-2)%2==0, u=(sq-2)\2; listput(L, u*(u+1)/2))); Vec(L)
%Y A298462 Cf. A000040, A000217, A061275, A298463, A298464, A298465, A298466.
%K A298462 nonn
%O A298462 1,1
%A A298462 _Colin Barker_, Jan 19 2018