cp's OEIS Frontend

A240718 Number of decompositions of 2n into an unordered sum of two primes, one of the two primes less than sqrt(2n-2).

%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