cp's OEIS Frontend

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

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