A002837 Numbers k such that k^2 - k + 41 is prime.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

Cf. A007634, A056561, A060566.

Programs

Magma

[n: n in [0..100] |IsPrime(n^2-n+41)]; // Vincenzo Librandi, Nov 21 2010

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 *)

PARI

v=[ ]; for(n=0,100, if(isprime(n^2-n+41),v=concat(v,n),)); v

Formula

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