A090111 Values of k such that {P(k), P(k+1), ..., P(k+6)} 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, 33, 45, 53, 66, 67, 84, 129, 130, 131, 266, 328, 329, 1619, 1620, 2655, 2937, 7509, 7510, 18030, 29283, 29714, 29715, 37630, 42037, 44473, 45905

Offset: 1

Author

Labos Elemer, Dec 30 2003

Keywords

• nonn

Comments

The terms are arguments providing a sequence of 7 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}, a 7-chain of primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..6400 (terms 1..200 from Harvey P. Dale)
• Carlos Rivera, Puzzle 232. Primes and Cubic polynomials, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A090101, A090102, A090107, A090108, A090109, A090110, A055561, A090563.

Programs

Mathematica

Flatten[Position[Partition[Table[If[PrimeQ[4n^2-154n+1523],1,0],{n,46000}],7,1],{1,1,1,1,1,1,1}]] (* Harvey P. Dale, Mar 06 2015 *)

PARI

isp(x) = isprime(4*x^2 - 154*x + 1523);
lista(kmax) = {my(v = vector(7, k, isp(k))); for(k = 8, kmax, if(vecprod(v) == 1, print1(k - 7, ", ")); v = concat(vecextract(v, "^1"), isp(k)));} \\ Amiram Eldar, Sep 27 2024