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A141100 Number of unordered pairs of odd composite numbers that sum to 2n. 7
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 3, 1, 1, 3, 2, 1, 4, 1, 2, 5, 1, 3, 5, 1, 4, 5, 3, 3, 6, 3, 3, 7, 3, 3, 9, 3, 4, 7, 4, 6, 9, 5, 5, 8, 6, 6, 10, 5, 5, 12, 4, 6, 12, 5, 9, 11, 7, 7, 11, 9, 9, 13, 8, 8, 16, 7, 11, 14, 8, 11, 14, 9, 9, 17, 13, 10, 16, 11, 11, 19, 11, 12, 18, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

COMMENTS

See A141099 for pairs of odd nonprime numbers. We have a(n) > 0 except for the 14 values of 2n given in A118081.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

a(n) = 1 - floor(n/2) + sum_{i=3..n} A005171(i) * A005171(2n-i), n>1. - Wesley Ivan Hurt, Dec 27 2013

EXAMPLE

a(18)=2 because 36 = 9+27 = 15+21.

MATHEMATICA

Table[cnt=0; Do[If[ !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i, 3, n, 2}]; cnt, {n, 100}]

CROSSREFS

Cf. A141095, A141097.

Sequence in context: A238406 A058709 A025842 * A270655 A229140 A280317

Adjacent sequences:  A141097 A141098 A141099 * A141101 A141102 A141103

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 02 2008, Jun 05 2008

STATUS

approved

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Last modified April 23 05:42 EDT 2021. Contains 343199 sequences. (Running on oeis4.)