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A090100 Numbers n such that n and the four successive integers produce primes if substituted for x in the polynomial 5x^2+5x+1. See A090562, A090563. Terms show that longer similar chains also exist.

%I A090100 #11 May 04 2024 02:11:26
%S A090100 1,2,3,13,266,321,322,323,344,641,1324,5436,16700,16701,19857,19858,
%T A090100 28151,28152,30648,31253,32045,45773,48710,50923,52397,57357,57358,
%U A090100 63879,63880,63881,72615,73164,73165,78785,81831,87640,87641,91116
%N A090100 Numbers n such that n and the four successive integers produce primes if substituted for x in the polynomial 5x^2+5x+1. See A090562, A090563. Terms show that longer similar chains also exist.
%C A090100 For examples of longer similar chains, if n = 1, 321, or 63879, the polynomial produces 7 consecutive prime terms (including n). - _Harvey P. Dale_, May 04 2024
%t A090100 Do[s=5*n^2+5*n+1;s1=5*(n+1)^2+5*(n+1)+1; s2=5*(n+2)^2+5*(n+2)+1;s3=5*(n+3)^2+5*(n+3)+1; s4=5*(n+4)^2+5*(n+4)+1; If[PrimeQ[s]&&PrimeQ[s1]&&PrimeQ[s2]&& PrimeQ[s3]&&PrimeQ[s4], Print[n]], {n, 1, 100000}]
%t A090100 SequencePosition[Table[If[PrimeQ[5n^2+5n+1],1,0],{n,100000}],{1,1,1,1,1}][[;;,1]] (* _Harvey P. Dale_, May 04 2024 *)
%Y A090100 Cf. A090562, A090563.
%K A090100 easy,nonn
%O A090100 1,2
%A A090100 _Labos Elemer_, Dec 12 2003