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Primes p for which p^2 + p - 1 = q*r (q<r) such that q, r, p^2 + q - 1 and p^2 + r - 1 are primes.
2

%I #10 Jul 08 2013 04:07:34

%S 7,17,23,61,67,71,79,151,307,311,383,389,409,439,613,677,1559,1627,

%T 1637,2377,2719,2801,3407,3821,4229,4799,4919,5557,5641,5743,5779,

%U 5851,5867,6133,6733,7121,7723,8009,8527,8573,10163,10729,11317,11789,11987,14107,14629,14653,14669,17189,17401,18077

%N Primes p for which p^2 + p - 1 = q*r (q<r) such that q, r, p^2 + q - 1 and p^2 + r - 1 are primes.

%H Peter J. C. Moses, <a href="/A227276/b227276.txt">Table of n, a(n) for n = 1..5000</a>

%F A226770(a^2(n) - 1) = 3.

%t Select[Prime[Range[3000]],And@@PrimeQ[#1^2-1+First[#2]]&&Last[#2]=={1,1}&[#1,Transpose[FactorInteger[#^2+#-1]]]&] (* _Peter J. C. Moses_, Jul 05 2013 *)

%Y Cf. A227129, A226770.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jul 04 2013

%E More terms from _Peter J. C. Moses_.

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