A353136 Primes whose gaps to both neighbor primes are triangular numbers.

53, 157, 173, 251, 257, 263, 337, 373, 547, 557, 563, 577, 587, 593, 607, 653, 733, 947, 977, 1039, 1103, 1123, 1181, 1187, 1223, 1367, 1627, 1747, 1753, 1907, 2017, 2063, 2287, 2417, 2677, 2719, 2897, 2903, 2963, 3307, 3313, 3517, 3547, 3637, 3733, 4013, 4211

Offset: 1

Author

Alois P. Heinz, Apr 25 2022

Keywords

• nonn

Examples

			Prime 251 is a term, the gap to the previous prime 241 is 10 and the gap to the next prime 257 is 6 and both gaps are triangular numbers.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A014494, A353088, A353135, A353137.

Programs

Maple

t:= proc(n) option remember; issqr(8*n+1) end:
q:= n-> isprime(n) and andmap(t, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..5000])[];

Mathematica

t[n_] := IntegerQ@Sqrt[8n+1];
q[n_] := PrimeQ[n] && t[n-NextPrime[n, -1]] && t[NextPrime[n]-n];
Select[Range[3, 5000], q] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)