A356293 Primes p such that if q is the next prime, (p+q)/6 is a triangular number.

7, 17, 29, 43, 107, 163, 197, 313, 457, 569, 757, 827, 1303, 1487, 1783, 1997, 2339, 2707, 2969, 3527, 3673, 3967, 4289, 4787, 5119, 5857, 7243, 9007, 9719, 10457, 10709, 10957, 12281, 13679, 16067, 17657, 20357, 21773, 23623, 27127, 27539, 31319, 33073, 33521, 37201, 38153, 45673, 48869, 50503

Offset

1,1

Comments

Primes p such that, if q is the next prime, 1+4*(p+q)/3 is a square.

Links

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

Example

a(3) = 29 is a term because 29 is prime, the next prime is 31, and (29+31)/6 = 10 is a triangular number.

Maple

P:= select(isprime, [seq(i, i=3..10^5, 2)]):
S:= (P[1..-2]+P[2..-1])/3:
P[select(i -> S[i]::integer and issqr(1+4*S[i]), [$1..nops(S)])];

Mathematica

Select[Partition[Prime[Range[5000]], 2, 1], IntegerQ[Sqrt[4*Total[#]/3 + 1]] &][[;; , 1]] (* Amiram Eldar, Aug 03 2022 *)

Crossrefs

Cf. A000217.

Sequence in context: A217926 A250294 A157417 * A294133 A088566 A059845

Adjacent sequences: A356290 A356291 A356292 * A356294 A356295 A356296

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 02 2022

Status

approved