%I #10 Jan 20 2018 02:41:39

%S 15,45,66,276,861,1128,1891,2556,3486,4005,5995,7140,7381,15051,20706,

%T 21528,24090,26796,28680,34716,46665,52975,56280,69006,74305,83028,

%U 83845,98346,102831,103740,109278,110215,112101,135981,148785,150975,176121,179700

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

%H Robert Israel, <a href="/A298462/b298462.txt">Table of n, a(n) for n = 1..10000</a>

%e 45 is in the sequence because 45+55 (consecutive triangular numbers) = 100 = 47+53 (consecutive primes).

%p f:= proc(n) local p,q;

%p p:= prevprime(floor((n+1)^2/2)); q:= nextprime(p);

%p if p+q = (n+1)^2 then n*(n+1)/2 else NULL fi

%p end proc:

%p map(f, [$2..1000]); # _Robert Israel_, Jan 19 2018

%o (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 Cf. A000040, A000217, A061275, A298463, A298464, A298465, A298466.

%K nonn

%O 1,1

%A _Colin Barker_, Jan 19 2018