A096139 Number of ways to write 2*n as an ordered sum of two numbers which are prime or 1.

1, 3, 3, 4, 3, 4, 5, 4, 6, 6, 5, 8, 5, 4, 8, 6, 7, 8, 5, 6, 10, 8, 7, 12, 8, 6, 12, 6, 7, 14, 7, 10, 12, 6, 10, 14, 11, 10, 14, 10, 9, 18, 9, 8, 20, 8, 9, 14, 8, 12, 18, 12, 11, 18, 14, 14, 22, 12, 11, 24, 7, 10, 20, 8, 14, 20, 11, 10, 18, 16, 15, 22, 11, 10, 26, 10, 16, 22, 11, 16, 20, 12

Offset: 1

Author

David Stroup, Jul 23 2004

Keywords

• easy
• nonn

Comments

A001031(n) = floor((a(n)+1)/2); a(n) mod 2 = A010051(n). - Reinhard Zumkeller, Aug 28 2013

Examples

			a(2)=3 because 4=1+3 or 4=2+2 or 4=3+1;
a(3)=3 because 6=1+5 or 6=3+3 or 6=5+1;
a(4)=4 because 8=1+7 or 8=3+5 or 8=5+3 or 8=7+1;
a(5)=3 because 10=3+7 or 10=5+5 or 10=7+3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A008578, A010051, A001031, A347744.

Programs

Haskell

a096139 n = sum (map a010051 gs') + fromEnum (1 `elem` gs')
   where gs' = map (2 * n -) $ takeWhile (< 2 * n) a008578_list
-- Reinhard Zumkeller, Aug 28 2013

PARI

{ a(n) = local(s(n) = if(n==1,1,isprime(n))); sum(i=1,2*n,s(i)*s(2*n-i)); } \\ Christian Krause, Dec 06 2022

Extensions

Example extended and typo fixed by Reinhard Zumkeller, Aug 28 2013