A238203 Squares s such that s^2+s+41 is prime.

1, 4, 9, 16, 25, 36, 64, 100, 144, 169, 196, 225, 324, 400, 441, 484, 529, 576, 625, 841, 900, 961, 1089, 1444, 1521, 1849, 2209, 2601, 2704, 2809, 3025, 3136, 3249, 3364, 3721, 3844, 4096, 4225, 4356, 4489, 5476, 5625, 5776, 6241, 7056, 7921, 8464, 8836, 9025

Offset: 1

Author

K. D. Bajpai, Feb 20 2014

Keywords

• nonn

Comments

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

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

Examples

			9 is in the sequence because 9 = 3^2 and 9^2+9+41 = 131 is prime.
36 is in the sequence because 36 = 6^2 and 36^2+36+41 = 1373 is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..4285

Crossrefs

Cf. A000040, A097823, A238242.

Programs

Maple

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);

Mathematica

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}];
Select[Range[100]^2,PrimeQ[#^2+#+41]&] (* Harvey P. Dale, Dec 13 2021 *)