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

1,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A044766 A342450 A160058 * A053070 A140655 A142508

Adjacent sequences: A353133 A353134 A353135 * A353137 A353138 A353139

Keyword

nonn

Author

Alois P. Heinz, Apr 25 2022

Status

approved