A007634 Numbers k such that k^2 + k + 41 is composite.

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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

Cf. A002837, A055390, A201998.

Programs

Magma

[n: n in [0..220] | not IsPrime(n^2 + n + 41)]; // Vincenzo Librandi, Sep 28 2012

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 *)

PARI

is(n)=!isprime(n^2+n+41) \\ Charles R Greathouse IV, Apr 25 2014

Formula

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