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First member of a prime quadruple in a p^2+p-1 progression.
3

%I #27 Aug 14 2024 16:54:33

%S 3,11,53,1693,2663,4423,16831,17609,36229,49801,94961,121493,150869,

%T 176303,183761,188011,210901,213833,218579,272903,300301,329671,

%U 439511,444791,453023,469613,518813,531911,546071,559703,570719,614279,705781

%N First member of a prime quadruple in a p^2+p-1 progression.

%C I found only one prime 5-tuple so far: (3,11,131,17291,298995971).

%C Subsequence of A057324. - _Pierre CAMI_, Sep 13 2013

%H Pierre CAMI, <a href="/A057325/b057325.txt">Table of n, a(n) for n = 1..6778</a>

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

%e 3 -> 3^2+3-1 = 11 -> 11^2+11-1 = 131 -> 131^2+131-1 = 17291 hence the quadruple (3,11,131,17291).

%t okQ[n_] := And@@PrimeQ/@NestList[#^2 + # - 1 &, n, 3];

%t Select[ Prime[ Range[ 60000]], okQ] (* _Harvey P. Dale_, Jan 05 2011 *)

%o (PARI) is(n)=for(k=1,4,if(!isprime(n),return(0));n=n^2+n-1);1 \\ _Charles R Greathouse IV_, Sep 13 2013

%Y Cf. A053184, A053185, A057324.

%K nonn

%O 1,1

%A _Patrick De Geest_, Aug 15 2000

%E Offset changed by _Andrew Howroyd_, Aug 14 2024