

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
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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^2k)^2k)^2xk)/(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

Table of n, a(n) for n=1..67.
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<3isprime(k^2*(k2)+k1)}, [0..200])
(Magma) [0, 1, 2] cat [n: n in [0..220]  IsPrime((n^2*(n2)+n1))]; // 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



