A007634 Numbers k such that k^2 + k + 41 is composite. (Formerly M5269)

40, 41, 44, 49, 56, 65, 76, 81, 82, 84, 87, 89, 91, 96, 102, 104, 109, 117, 121, 122, 123, 126, 127, 130, 136, 138, 140, 143, 147, 155, 159, 161, 162, 163, 164, 170, 172, 173, 178, 184, 185, 186, 187, 190, 201, 204, 205, 207, 208, 209, 213, 215, 216, 217

Offset

1,1

Comments

A subset of this sequence is shown in A055390. - Matt C. Anderson, Jan 05 2014

If prime p divides m^2+m+41, then m+p*j is in the sequence for all j >= 1. - Robert Israel, Nov 24 2017

Euler noted that the first 40 values of this polynomial, starting with k=0, are all primes. - Harvey P. Dale, Jul 25 2023

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Formula

a(n) ~ n. - Charles R Greathouse IV, Apr 25 2014

Maple

remove(n -> isprime(n^2+n+41), [$1..1000]); # Robert Israel, Nov 24 2017

Mathematica

Select[Range[220], !PrimeQ[#^2 + # + 41] &] (* Vincenzo Librandi, Sep 28 2012 *)

Prog

(Magma) [n: n in [0..220] | not IsPrime(n^2 + n + 41)]; // Vincenzo Librandi, Sep 28 2012
(PARI) is(n)=!isprime(n^2+n+41) \\ Charles R Greathouse IV, Apr 25 2014

Crossrefs

Cf. A002837, A055390, A201998.

Sequence in context: A273770 A165861 A082763 * A228184 A128843 A214563

Adjacent sequences: A007631 A007632 A007633 * A007635 A007636 A007637

Keyword

nonn,easy

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Status

approved