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%I #8 Apr 02 2020 19:00:19
%S 1,321,63879,6265151,6921510,9239188,23156113,26854544,35917576,
%T 45591317,51307313,52260254,53855078,71731838,118305552,124220571,
%U 124234464,150767861,170448863,192850264
%N Numbers n such that n and the 6 successive integers yield primes if substituted for x in polynomial 5x^2+5x+1.
%e a[15]=118305552 and the corresponding seven "polynomially consecutive" primes are: {69981018761651281, 69981019944706811, 69981021127762351, 69981022310817901, 69981023493873461, 69981024676929031, 69981025859984611}
%t po[x_] := 5*x^2+5*x+1 Do[s=po[n];s0=po[n];s1=po[n+1];s2=po[n+2];s3=po[n+3];s4=po[n+4]; s5=po[n+5];s6=po[n+6];If[IntegerQ[n/100000], Print[{n}]]; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3]&&PrimeQ[s4]&&PrimeQ[s5] &&PrimeQ[s6], Print[{n, s0, s1, s2, s3, s4, s5, s6}]], {n, 1, 120000000}]
%t Select[Range[193*10^6],AllTrue[Table[5x^2+5x+1,{x,Range[#,#+6]}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 02 2020 *)
%Y Cf. A090562, A090563, A090100, A090102.
%K nonn
%O 1,2
%A _Labos Elemer_, Dec 12 2003
%E More terms from _Don Reble_, Dec 14 2003