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 A090106 Values of n such that P[n]=n^2+n+41 is prime and also {P[n+1],...,P[n+13-1]} are prime numbers. Namely: a(n)= the first argument providing 13 "polynomially consecutive" primes with respect of polynomial=x^2+x+41. 0

%I

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,52,61,219

%N Values of n such that P[n]=n^2+n+41 is prime and also {P[n+1],...,P[n+13-1]} are prime numbers. Namely: a(n)= the first argument providing 13 "polynomially consecutive" primes with respect of polynomial=x^2+x+41.

%e a(n)=219: {P,..,P}={48221,...,53633}, i.e. 13 consecutive integer values substituted to P[x]=x^2+x+41 polynomial, all provide primes; the "classical case" include one single 41-chain of PC-primes, see A055561.

%t po[x_] := x^2+x+41 Do[s=po[n];s0=po[n];s1=po[n+1]; s2=po[n+2];s3=po[n+3];s4=po[ +4];s5=po[n+5]; s6=po[n+6];s7=po[n+7];s8=po[n+8];s9=po[n+9]; s10=po[n+10];s11=po[n+11];s12=po[n+12]; If[IntegerQ[n/100000], Print[{n}]]; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3] &&PrimeQ[s4]&&PrimeQ[s5]&&PrimeQ[s6]&&PrimeQ[s7]&&PrimeQ[s8]&& PrimeQ[s9]&&PrimeQ[s10]&&PrimeQ[s11]&&PrimeQ[s12], Print[{n, s0, s1, s11, s12}]], {n, 1, 600000}]

%Y Cf. A055561, A090562, A090563, A090101, A090102.

%K nonn

%O 1,2

%A _Labos Elemer_, Dec 22 2003

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)