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

Author

K. D. Bajpai, May 08 2014

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)