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

1,1

Links

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

Example

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

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

Prog

(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)

Crossrefs

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

Sequence in context: A293625 A084821 A345654 * A066763 A164788 A033849

Adjacent sequences: A298459 A298460 A298461 * A298463 A298464 A298465

Keyword

nonn

Author

Colin Barker, Jan 19 2018

Status

approved