A242230 Primes p of the form p^2 + q + 1 where p < q are consecutive primes.

61, 4561, 9511, 17299, 19471, 26737, 30109, 37447, 49957, 69439, 94561, 196699, 209311, 259603, 317539, 333517, 352249, 414097, 427069, 459013, 678157, 845491, 886429, 943819, 1027189, 1217719, 1410163, 1472587, 1647379, 2165323, 2200777, 2230549, 2603389

Offset: 1

Author

K. D. Bajpai, May 08 2014

Keywords

• nonn

Examples

			a(1) = 61 = 7^2 + 11 + 1: 61 is prime, 7 and 11 are consecutive primes.
a(2) = 4561 = 67^2 + 71 + 1: 4561 is prime, 67 and 71 are consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..7040

Crossrefs

Cf. A242231, A000040, A241945, A045636, A214723, A214511.

Programs

Maple

with(numtheory): A242230:= proc()local k ; k:=(ithprime(x)^2+ithprime(x+1)+1); if  isprime(k) then RETURN (k); fi;end: seq(A242230 (),x=1..500);

Mathematica

A242230 = {}; Do[p = Prime[n]^2 + Prime[n + 1] + 1; If[PrimeQ[p], AppendTo[A242230, p]], {n, 500}]; A242230
Select[#[[1]]^2+#[[2]]+1&/@Partition[Prime[Range[300]],2,1],PrimeQ] (* Harvey P. Dale, Mar 28 2016 *)