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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 Cf. A027445, A144051, A187057, A187058, A187060, A190800, A191456, A191457, A191458, A247949, A247966, A248206. Sequence in context: A162181 A162412 A010995 * A288031 A265658 A214100 Adjacent sequences: A253912 A253913 A253914 * A253916 A253917 A253918 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.)