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A352100 Number of partitions of 2n into two odd parts that are not both prime. 0
1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 5, 5, 8, 7, 7, 8, 8, 7, 9, 10, 9, 11, 11, 9, 13, 11, 11, 15, 13, 12, 14, 14, 13, 16, 16, 13, 17, 18, 14, 19, 19, 17, 22, 19, 18, 21, 21, 19, 22, 21, 19, 23, 24, 18, 27, 26, 22, 29, 26, 24, 28, 29, 27, 28, 28, 25, 31, 32, 26, 34, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
FORMULA
a(1) = a(2) = 1, a(n) = ceiling(n/2) - A045917(n), n >= 3.
EXAMPLE
a(17) = 5; There are 5 partitions of 2*17 = 34 into two odd parts that are not both prime: 34 = 1+33 = 7+27 = 9+25 = 13+21 = 15+19.
MATHEMATICA
a[1] = a[2] = 1; a[n_] := Ceiling[n/2] - Count[2*n - Prime[Range[PrimePi[n]]], _?PrimeQ]; Array[a, 100] (* Amiram Eldar, May 12 2022 *)
CROSSREFS
Cf. A045917.
Sequence in context: A216503 A216672 A104055 * A216200 A157873 A022870
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 05 2022
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)