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A253915 Primes p such that the polynomial k^4 + k^3 + k^2 + k + p yields primes for k = 0..8, but not for k = 9. 2
43, 967, 11923, 213943, 2349313, 3316147, 30637567, 33421159, 39693817, 49978447, 105963769, 143405887, 148248949, 153756073, 156871549, 172981279, 187310803, 196726693, 203625283, 211977523, 220825453, 268375879, 350968543, 357834283, 414486697, 427990369 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All the terms in this sequence are congruent to 1 (mod 3).
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..155 (terms < 2*10^10)
EXAMPLE
a(1) = 43:
0^4 + 0^3 + 0^2 + 0 + 43 = 43;
1^4 + 1^3 + 1^2 + 1 + 43 = 47;
2^4 + 2^3 + 2^2 + 2 + 43 = 73;
3^4 + 3^3 + 3^2 + 3 + 43 = 163;
4^4 + 4^3 + 4^2 + 4 + 43 = 383;
5^4 + 5^3 + 5^2 + 5 + 43 = 823;
6^4 + 6^3 + 6^2 + 6 + 43 = 1597;
7^4 + 7^3 + 7^2 + 7 + 43 = 2843;
8^4 + 8^3 + 8^2 + 8 + 43 = 4723;
all nine are primes, and
9^4 + 9^3 + 9^2 + 9 + 43 = 7423 = 13*571 is composite.
The next prime for p=43 appears for k=13, namely 30983.
MATHEMATICA
Select[Prime[Range[118*10^5]], AllTrue[#+{0, 4, 30, 120, 340, 780, 1554, 2800, 4680}, PrimeQ]&&CompositeQ[#+7380]&] (* Harvey P. Dale, Sep 10 2021 *)
PROG
(PARI) forprime(p=1, 1e10, if(isprime(p+4)&& isprime(p+30)&& isprime(p+120)&& isprime(p+340)&& isprime(p+780)&& isprime(p+1554)&& isprime(p+2800)&& isprime(p+4680) && !isprime(p+7380), print1(p, ", ")))
CROSSREFS
Sequence in context: A162181 A162412 A010995 * A288031 A265658 A214100
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jan 18 2015
EXTENSIONS
Edited by Wolfdieter Lang, Feb 20 2015
Corrected and extended by Harvey P. Dale, Sep 10 2021
STATUS
approved

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Last modified May 18 03:12 EDT 2024. Contains 372617 sequences. (Running on oeis4.)