A175132 -id:A175132 - cp's OEIS frontend

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

Alex Ratushnyak, May 28 2013

nonn

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

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).

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

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 *)

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

cp's OEIS Frontend

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

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