A225077 Smaller of the two consecutive primes whose sum is a triangular number.

17, 37, 59, 103, 137, 149, 313, 467, 491, 883, 911, 1277, 1423, 1619, 1783, 2137, 2473, 2729, 4127, 4933, 5437, 5507, 6043, 6359, 10039, 10453, 11717, 13397, 15809, 17489, 20807, 21821, 23027, 27631, 28307, 28813, 29669, 33029, 36947, 39103, 44203, 48281

Offset

1,1

Links

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

Formula

a(n) + nextprime(a(n)) = A000217(A175132(n)).

Maple

f:= proc(n) local m, p, q;
  m:= n*(n+1)/2;
  p:= prevprime(ceil(m/2));
  q:= nextprime(p);
  if p+q=m then p fi
end proc:
map(f, [$3..500]); # Robert Israel, May 04 2020

Mathematica

tri[n_] := IntegerQ[Sqrt[1 + 8 n]]; t = {}; p1 = 2; While[Length[t] < 50, p2 = NextPrime[p1]; If[tri[p1 + p2], AppendTo[t, p1]]; p1 = p2]; t (* T. D. Noe, May 28 2013 *)

Crossrefs

Cf. A175132 (numbers n such that sum of two consecutive primes is triangular(n)).

Cf. A181902 and A154634 (average of two consecutive primes is a triangular number).

Cf. A075190 and A225195 (average of two consecutive primes is a square).

Cf. A074924 and A061275 (sum of two consecutive primes is a square).

Sequence in context: A295338 A059425 A341937 * A146328 A161549 A269788

Adjacent sequences: A225074 A225075 A225076 * A225078 A225079 A225080

Keyword

nonn

Author

Alex Ratushnyak, May 28 2013

Status

approved