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 A071635 #19 Dec 17 2021 07:35:59
%S A071635 0,0,1,0,1,1,1,1,2,0,2,2,1,2,3,0,3,2,2,3,2,1,3,2,1,4,3,2,5,3,2,5,3,2,
%T A071635 3,4,2,5,4,1,5,3,3,4,4,1,6,4,3,6,5,2,9,3,3,4,4,2,6,4,2,8,4,4,5,4,3,8,
%U A071635 5,2,7,7,4,9,6,3,7,6,3,6,6,2,12,5,4,8,6,5,10,4,2,10,7,4
%N A071635 Number of decompositions of 4*n+2 into sum of two primes of form 4*k+1.
%C A071635 For a(m)=0 see A071636.
%H A071635 Andrew Howroyd, <a href="/A071635/b071635.txt">Table of n, a(n) for n = 0..10000</a>
%H A071635 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>.
%F A071635 a(n) = A002375(2*n+1) - A156642(n). - _Vladimir Shevelev_, Feb 12 2009
%e A071635 a(10)=2 as 4*10+2 = 42 = 5+37 = (4*1+1)+(4*9+1) = 13+29 = (4*3+1)+(4*7+1) and the other two decompositions 42 = 11+31 = (4*2+3)+(4*7+3) = 19+23 = (4*4+3)+(4*5+3), A002375(21)=4.
%t A071635 a[n_] := Module[{s = 0}, For[p = 3, p <= 2n+1, p = NextPrime[p], If[Mod[p, 4] == 1 && PrimeQ[4n+2-p], s++]]; s];
%t A071635 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Dec 17 2021, after _Andrew Howroyd_ *)
%o A071635 (PARI) a(n)={my(s=0); forprime(p=3, 2*n+1, if(p%4==1 && isprime(4*n+2-p), s++)); s} \\ _Andrew Howroyd_, Feb 02 2020
%Y A071635 Cf. A002375, A002144, A071636, A156642.
%K A071635 nonn,look
%O A071635 0,9
%A A071635 _Reinhard Zumkeller_, May 27 2002