This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A125257 #11 Jan 17 2025 14:51:08
%S A125257 7,19,13,67,103,7,199,7,109,13,487,193,7,787,7,13,19,433,1447,7,19,7,
%T A125257 13,769,2503,2707,7,43,7,1201,3847,4099,1453,7,4903,7,5479,5779,2029,
%U A125257 19,7,13,7,61,37,8467,8839,7,13,7,3469,31,11239,3889,7,12547,7,43,19,4801
%N A125257 Smallest prime divisor of 4n^2+3 that is of the form 6k+1.
%C A125257 Any prime divisor of 4n^2+3 different from 3 is congruent to 1 modulo 6.
%C A125257 4n^2+3 is never a power of 3 for n > 0; hence a prime divisor congruent to 1 modulo 6 always exists.
%C A125257 a(n) = 7 if and only if n is congruent to 1 or -1 modulo 7.
%D A125257 D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.
%H A125257 Nick Hobson, <a href="/A125257/b125257.txt">Table of n, a(n) for n = 1..1000</a>
%e A125257 The prime divisors of 4*3^2+3=39 are 3 and 13, so a(3) = 13.
%t A125257 Table[SelectFirst[FactorInteger[4 n^2+3][[;;,1]],Mod[#,6]==1&],{n,60}] (* _Harvey P. Dale_, Jan 17 2025 *)
%o A125257 (PARI) vector(60, n, factor(4*n^2+3)[2-(n^2)%3,1])
%Y A125257 Cf. A057204, A124988.
%K A125257 easy,nonn
%O A125257 1,1
%A A125257 _Nick Hobson_, Nov 26 2006