%I M0473 N0174 #58 Sep 08 2022 08:44:31
%S 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,
%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43,44,46,47,48,49,51,52,
%U 53,54,55,56,58,59,60,61,62,63,64,65,67,68,69,70,71,72
%N Numbers k such that k^2 - k + 41 is prime.
%C Leonhard Euler published this prime-generating formula in 1772. - _Harvey P. Dale_, Sep 23 2020
%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002837/b002837.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A056561(n-1) + 1, n > 1. - _Robert Price_, Nov 08 2019
%p A002837:=n->`if`(isprime(n^2-n+41),n,NULL): seq(A002837(n), n=0..100); # _Wesley Ivan Hurt_, Oct 21 2014
%t Select[Range[0,100],PrimeQ[#^2-#+41]&] (* _Harvey P. Dale_, May 27 2012 *)
%o (PARI) v=[ ]; for(n=0,100, if(isprime(n^2-n+41),v=concat(v,n),)); v
%o (Magma) [n: n in [0..100] |IsPrime(n^2-n+41)]; // _Vincenzo Librandi_, Nov 21 2010
%Y Cf. A007634, A056561, A060566.
%K nonn,nice,easy
%O 1,3
%A _N. J. A. Sloane_