A090110 Values of n such that P[n]=4n^2-154n+1523 is prime and also {P[n+1],...,P[n+8-1]} are prime numbers. Namely: the terms are arguments introducing a sequence of 8 polynomially consecutive primes with respect to 4x^2-154x+1523 polynomial communicated by Rivera (2003).

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, 28, 29, 30, 31, 32, 66, 129, 130, 328, 1619, 7509, 29714, 45905, 447588, 509862

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Example

n=1 provides {1373, 1231, 1097, 971, 853, 743, 641, 547} 8-chain of primes.

Mathematica

po[x_] := 4*x^2-154*x+1523; Do[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]; s7=po[n+7]; If[PrimeQ[s0]&&PrimeQ[s1] &&PrimeQ[s2]&&PrimeQ[s3]&&PrimeQ[s4]&&PrimeQ[s5]&&PrimeQ[s6] &&PrimeQ[s7], Print[n]], {n, 1, 1000000}]
okQ[x_] := And@@PrimeQ[Table[4n^2-154n+1523, {n, x, x+7}]]; Select[Range[ 510000], okQ] (* Harvey P. Dale, May 25 2011 *)

Crossrefs

Cf. A090101, A090102, A090107-A090109, A055561, A090563.

Sequence in context: A071669 A114086 A257333 * A166718 A132016 A032513

Adjacent sequences: A090107 A090108 A090109 * A090111 A090112 A090113

Keyword

nonn

Author

Labos Elemer, Dec 30 2003

Status

approved