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

%I #16 Mar 28 2016 09:11:53

%S 61,4561,9511,17299,19471,26737,30109,37447,49957,69439,94561,196699,

%T 209311,259603,317539,333517,352249,414097,427069,459013,678157,

%U 845491,886429,943819,1027189,1217719,1410163,1472587,1647379,2165323,2200777,2230549,2603389

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

%H K. D. Bajpai, <a href="/A242230/b242230.txt">Table of n, a(n) for n = 1..7040</a>

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

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

%p 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);

%t A242230 = {}; Do[p = Prime[n]^2 + Prime[n + 1] + 1; If[PrimeQ[p], AppendTo[A242230, p]], {n, 500}]; A242230

%t Select[#[[1]]^2+#[[2]]+1&/@Partition[Prime[Range[300]],2,1],PrimeQ] (* _Harvey P. Dale_, Mar 28 2016 *)

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

%K nonn

%O 1,1

%A _K. D. Bajpai_, May 08 2014