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.

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, 27, 52, 61, 219

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Example

a(n)=219: {P[219],..,P[231]}={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.

Mathematica

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}]

Crossrefs

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

Sequence in context: A352800 A154470 A194907 * A369464 A167662 A309810

Adjacent sequences: A090103 A090104 A090105 * A090107 A090108 A090109

Keyword

nonn

Author

Labos Elemer, Dec 22 2003

Status

approved