OFFSET
1,2
COMMENTS
a(n) is the first argument providing 11 "polynomially consecutive" primes with respect to the polynomial x^2 - 79*x + 1601 described by Escott in 1899.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..83
E. B. Escott, Réponse 1133, Formule d'Euler x^2 + x + 41 et formules analogues, L'Intermédiaire des mathématiciens, Vol. 6 (1899), pp. 10-11.
EXAMPLE
k = 1 provides the following non-monotonic (!) chain of 11 "polynomially consecutive" primes as follows: {1523, 1447, 1373, 1301, 1231, 1163, 1097, 1033, 971, 911, 853}.
MATHEMATICA
Position[Times @@@ Partition[Table[Boole@PrimeQ[k^2 - 79*k + 1601], {k, 1, 1000}], 11, 1], 1] // Flatten (* Amiram Eldar, Sep 27 2024 *)
PROG
(PARI) isp(x) = isprime(x^2 - 79*x + 1601);
lista(kmax) = {my(v = vector(11, k, isp(k))); for(k = 12, kmax, if(vecprod(v) == 1, print1(k - 11, ", ")); v = concat(vecextract(v, "^1"), isp(k))); } \\ Amiram Eldar, Sep 27 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 29 2003
EXTENSIONS
Data corrected by Amiram Eldar, Sep 27 2024
STATUS
approved