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A096139
Number of ways to write 2*n as an ordered sum of two numbers which are prime or 1.
4
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
1,2
COMMENTS
A001031(n) = floor((a(n)+1)/2); a(n) mod 2 = A010051(n). - Reinhard Zumkeller, Aug 28 2013
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
David Stroup, Jul 23 2004
EXTENSIONS
Example extended and typo fixed by Reinhard Zumkeller, Aug 28 2013
STATUS
approved