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A090109
Values of k such that {P(k), P(k+1), ..., P(k+10)} are all prime numbers, where P(k) = k^2 - 79*k + 1601.
4
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, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 259, 260, 261
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 29 2003
EXTENSIONS
Data corrected by Amiram Eldar, Sep 27 2024
STATUS
approved