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

15, 45, 66, 276, 861, 1128, 1891, 2556, 3486, 4005, 5995, 7140, 7381, 15051, 20706, 21528, 24090, 26796, 28680, 34716, 46665, 52975, 56280, 69006, 74305, 83028, 83845, 98346, 102831, 103740, 109278, 110215, 112101, 135981, 148785, 150975, 176121, 179700

Offset: 1

Author

Colin Barker, Jan 19 2018

Keywords

• nonn

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A061275, A298463, A298464, A298465, A298466.

Programs

Maple

f:= proc(n) local p,q;
  p:= prevprime(floor((n+1)^2/2)); q:= nextprime(p);
  if p+q = (n+1)^2 then n*(n+1)/2 else NULL fi
end proc:
map(f, [$2..1000]); # Robert Israel, Jan 19 2018

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)