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 A240718 #17 Oct 02 2023 20:15:10 %S A240718 0,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,2,1,0,1,1,1,2,1,1,1,1,1,1,1,1,2,2,1, %T A240718 1,1,2,2,2,1,1,1,2,1,1,1,1,1,0,1,1,2,2,2,2,2,2,2,1,1,0,1,0,0,1,1,2,1, %U A240718 2,1,3,2,1,1,1,1,2,2,1,2,2,1,1,2,2,1,2,2,2,2,1,3,3,1,1,2,2,2,2,2 %N A240718 Number of decompositions of 2n into an unordered sum of two primes, one of the two primes less than sqrt(2n-2). %H A240718 Robert Israel, <a href="/A240718/b240718.txt">Table of n, a(n) for n = 1..10000</a> %e A240718 For n = 7, the a(7) = 1 solution is 2*7 = 3 + 11 = 7 + 7; one of these pairs, 3 + 11, contains a number less than sqrt(2*7 - 2). %p A240718 P:= NULL: A[1]:= 0: nextp:= 2: %p A240718 for n from 2 to 100 do %p A240718 while nextp^2 < 2*n-2 do %p A240718 P:= P, nextp; %p A240718 nextp:= nextprime(nextp); %p A240718 od; %p A240718 A[n]:= numboccur(true, map(t -> isprime(2*n-t), [P])) %p A240718 od: %p A240718 seq(A[i],i=1..100); # _Robert Israel_, Apr 30 2019 %o A240718 (PARI) %o A240718 a(n)=sum(i=2,primepi(floor(sqrt(2*n-2))),isprime(2*n-prime(i))) \\ _Lear Young_, Apr 11 2014 %Y A240718 Cf. A002375. %K A240718 nonn %O A240718 1,17 %A A240718 _Lear Young_, Apr 11 2014