A238203 - OEIS

%I #25 Dec 13 2021 14:36:56

%S 1,4,9,16,25,36,64,100,144,169,196,225,324,400,441,484,529,576,625,

%T 841,900,961,1089,1444,1521,1849,2209,2601,2704,2809,3025,3136,3249,

%U 3364,3721,3844,4096,4225,4356,4489,5476,5625,5776,6241,7056,7921,8464,8836,9025

%N Squares s such that s^2+s+41 is prime.

%C n^2+n+41: Euler’s prime generating polynomial.

%C First 6 terms in the sequence are first 6 consecutive squares.

%H K. D. Bajpai, <a href="/A238203/b238203.txt">Table of n, a(n) for n = 1..4285</a>

%e 9 is in the sequence because 9 = 3^2 and 9^2+9+41 = 131 is prime.

%e 36 is in the sequence because 36 = 6^2 and 36^2+36+41 = 1373 is prime.

%p with(numtheory):KD := proc() local a,b; a:=(n^2);b:=a^2+a+41; if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..500);

%t Select[Table[k = n^2, {n, 100}], PrimeQ[#^2 + # + 41] &] (* or *) c = 0; Do[k = n^2; If[PrimeQ[k^2 + k + 41], c = c + 1; Print[c, " ", k]], {n, 1, 10000}];

%t Select[Range[100]^2,PrimeQ[#^2+#+41]&] (* _Harvey P. Dale_, Dec 13 2021 *)

%Y Cf. A000040, A097823, A238242.

%K nonn

%O 1,2

%A _K. D. Bajpai_, Feb 20 2014