A240718 - OEIS

%I #17 Oct 02 2023 20:15:10

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

%H Robert Israel, <a href="/A240718/b240718.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 P:= NULL: A[1]:= 0: nextp:= 2:

%p for n from 2 to 100 do

%p  while nextp^2 < 2*n-2 do

%p    P:= P, nextp;

%p    nextp:= nextprime(nextp);

%p  od;

%p  A[n]:= numboccur(true, map(t -> isprime(2*n-t), [P]))

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Apr 30 2019

%o (PARI)

%o a(n)=sum(i=2,primepi(floor(sqrt(2*n-2))),isprime(2*n-prime(i))) \\ _Lear Young_, Apr 11 2014

%Y Cf. A002375.

%K nonn

%O 1,17

%A _Lear Young_, Apr 11 2014