A242231 Primes p of the form p^2 + q - 1 where p < q are consecutive primes.

13, 31, 59, 307, 383, 557, 997, 1409, 1723, 3541, 5113, 5407, 6323, 6977, 8017, 10303, 19469, 52673, 94559, 109897, 151717, 158009, 187927, 193163, 249503, 274069, 326617, 361807, 383791, 419261, 427067, 546863, 573809, 592133, 636017, 684757, 735307, 738743

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..6900

Example

a(1) = 13 = 3^2 + 5 - 1: 13 is prime, 3 and 5 are consecutive primes.
a(2) = 31 = 5^2 + 7 - 1: 31 is prime, 5 and 7 are consecutive primes.

Maple

with(numtheory): A242231:= proc()local k ; k:=(ithprime(x)^2+ithprime(x+1)-1); if  isprime(k) then RETURN (k); fi; end: seq(A242231 (), x=1..500);

Mathematica

A242231 = {}; Do[p = Prime[n]^2 + Prime[n + 1] - 1; If[PrimeQ[p], AppendTo[A242231, p]], {n, 500}]; A242231
Select[#[[1]]^2+#[[2]]-1&/@Partition[Prime[Range[250]], 2, 1], PrimeQ] (* Harvey P. Dale, Mar 05 2022 *)

Crossrefs

Cf. A242230, A000040, A241945, A045636, A214723, A214511.

Sequence in context: A166143 A065768 A155820 * A330855 A268927 A061239

Adjacent sequences: A242228 A242229 A242230 * A242232 A242233 A242234

Keyword

nonn

Author

K. D. Bajpai, May 08 2014

Status

approved