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 A308981 Nonnegative integers k such that k^3 - 2*k^2 + k - 1 is not composite. 0
 0, 1, 2, 3, 5, 6, 7, 10, 12, 13, 15, 20, 23, 26, 27, 28, 30, 33, 35, 37, 38, 41, 45, 48, 50, 56, 61, 63, 65, 66, 70, 71, 72, 82, 83, 85, 90, 96, 98, 107, 108, 115, 120, 122, 126, 128, 133, 140, 141, 142, 145, 148, 156, 160, 162, 166, 173, 175, 180, 185, 191, 202, 205, 208, 213, 217, 220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Apart the three initial terms which lead to +/-1, all other terms lead to prime P(k) = k^3 - 2*k^2 + k - 1. The polynomial Q = (((x^2-k)^2-k)^2-x-k)/(x^2 - x - k) of degree 6 has two factors of degree <= 3 when k is in A014206. This can only happen when the constant term of Q, which equals -P(k), is not prime. Therefore, A014206 is a subsequence of the complement of this sequence. LINKS R. Israel, in reply to T. Baruchel, A014206 and computer algebra systems, SeqFan list, July 4, 2019. MATHEMATICA Join[{0, 1, 2}, Select[Range[230], PrimeQ[((#^2 (# - 2) + # - 1))] &]] (* Vincenzo Librandi, Jul 19 2019 *) PROG (PARI) select( is(k)={k<3||isprime(k^2*(k-2)+k-1)}, [0..200]) (Magma) [0, 1, 2] cat [n: n in [0..220] | IsPrime((n^2*(n-2)+n-1))]; // Vincenzo Librandi, Jul 19 2019 CROSSREFS Cf. A014206. Sequence in context: A357425 A090034 A037016 * A239746 A101323 A298705 Adjacent sequences: A308978 A308979 A308980 * A308982 A308983 A308984 KEYWORD nonn AUTHOR M. F. Hasler, Jul 04 2019 STATUS approved

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)