A002837 Numbers k such that k^2 - k + 41 is prime. (Formerly M0473 N0174)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72

Offset

1,3

Comments

Leonhard Euler published this prime-generating formula in 1772. - Harvey P. Dale, Sep 23 2020

References

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A056561(n-1) + 1, n > 1. - Robert Price, Nov 08 2019

Maple

A002837:=n->`if`(isprime(n^2-n+41), n, NULL): seq(A002837(n), n=0..100); # Wesley Ivan Hurt, Oct 21 2014

Mathematica

Select[Range[0, 100], PrimeQ[#^2-#+41]&] (* Harvey P. Dale, May 27 2012 *)

Prog

(PARI) v=[ ]; for(n=0, 100, if(isprime(n^2-n+41), v=concat(v, n), )); v
(Magma) [n: n in [0..100] |IsPrime(n^2-n+41)]; // Vincenzo Librandi, Nov 21 2010

Crossrefs

Cf. A007634, A056561, A060566.

Sequence in context: A247151 A267069 A366188 * A271143 A056561 A321993

Adjacent sequences: A002834 A002835 A002836 * A002838 A002839 A002840

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved