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 A257567 #16 Sep 21 2023 01:19:22
%S A257567 1,0,3,1,1,2,1,1,2,1,2,1,2,1,1,1,4,1,2,1,1,1,1,1,1,1,4,1,1,3,1,2,1,2,
%T A257567 2,1,3,1,3,1,1,1,1,2,1,1,3,1,1,2,1,2,1,1,2,1,1,1,1,1,2,2,1,2,1,1,1,2,
%U A257567 2,1,1,1,1,3,1,4,1,1,2,2,2,1,1,1,1,1,1,1,1,2,1,1,1,3,2,1,2
%N A257567 a(n) is the largest exponent k such that 3^k divides (prime(n)^2 + 2).
%C A257567 Except for n=2, all a(n) > 1 because (prime(n)^2 + 2) is divisible by 3.
%H A257567 Zak Seidov, <a href="/A257567/b257567.txt">Table of n, a(n) for n = 1..1000</a>
%F A257567 a(n) = A007949(A061725(n)). - _Michel Marcus_, May 01 2015
%e A257567 a(1) = 1 because p=prime(1)=2 and p^2 + 2 = 6 = 3^1*2,
%e A257567 a(2) = 0 because p=prime(2)=3 and p^2 + 2 = 11 = 3^0*11,
%e A257567 a(3) = 3 because p=prime(3)=5 and p^2 + 2 = 27 = 3^3.
%t A257567 Table[IntegerExponent[Prime[k]^2 + 2, 3], {k, 100}]
%o A257567 (PARI) a(n) = valuation(prime(n)^2+2, 3); \\ _Michel Marcus_, May 01 2015
%Y A257567 Cf. A007949 (3-adic valuation), A061725 (p^2+2, with p prime), A257568.
%K A257567 nonn
%O A257567 1,3
%A A257567 _Zak Seidov_, Apr 30 2015