A090110 Values of k such that {P(k), P(k+1), ..., P(k+7)} are all prime numbers, where P(k) = 4*k^2 - 154*k + 1523.

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, 1022565, 1102373, 1388125, 1665379, 1762387, 1786292, 2111602, 2962834, 3391838

Offset: 1

Author

Labos Elemer, Dec 30 2003

Keywords

• nonn

Comments

The terms are arguments introducing a sequence of 8 polynomially consecutive primes with respect to 4*x^2 - 154*x + 1523, a polynomial communicated by Rivera (2003).

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Carlos Rivera, Puzzle 232. Primes and Cubic polynomials, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A090101, A090102, A090107, A090108, A090109, A055561, A090563.

Programs

Mathematica

okQ[x_] := And@@PrimeQ[Table[4n^2-154n+1523, {n,x,x+7}]];
Select[Range[ 510000], okQ] (* Harvey P. Dale, May 25 2011 *)

PARI

isp(x) = isprime(4*x^2 - 154*x + 1523);
lista(kmax) = {my(v = vector(8, k, isp(k))); for(k = 9, kmax, if(vecprod(v) == 1, print1(k - 8, ", ")); v = concat(vecextract(v, "^1"), isp(k)));} \\ Amiram Eldar, Sep 27 2024

Extensions

a(43)-a(51) from Amiram Eldar, Sep 27 2024