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A062303 Number of ways writing n-th prime as a sum of a nonprime and a composite. 1
1, 0, 1, 1, 1, 2, 2, 3, 3, 5, 6, 7, 8, 9, 9, 11, 13, 14, 15, 16, 17, 18, 19, 21, 24, 25, 26, 26, 27, 27, 33, 34, 36, 37, 40, 41, 42, 44, 45, 47, 49, 50, 53, 54, 54, 55, 59, 64, 65, 66, 66, 68, 69, 72, 74, 76, 78, 79, 80, 81, 82, 85, 91, 92, 93, 93, 99, 101, 105, 106, 106, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..71.

FORMULA

A062610(A000040(n)) = number of [nonprime+composite] partitions of p(n).

EXAMPLE

n=10,p(10)=29 has 14 partitions of form a+b=29; 1+28=4+25=8+21=9+20=14+15 are the 5 relevant partitions, so a(10)=5.

MATHEMATICA

Table[c = 0; Do[If[i + j == Prime[n] && ! PrimeQ[i] && ! PrimeQ[j], c = c + 1], {i, Prime[n] - 1}, {j, i}]; c, {n, 72}] (* Jayanta Basu, Apr 22 2013 *)

cnpQ[{a_, b_}]:=(!PrimeQ[a]&&CompositeQ[b])||(!PrimeQ[b]&&CompositeQ[a]); Join[{1}, Table[Length[Select[IntegerPartitions[Prime[n], {2}], cnpQ]], {n, 2, 80}]] (* Harvey P. Dale, Sep 30 2018 *)

CROSSREFS

Cf. A061358, A062602, A062610, A000040, A014092, A025584.

Sequence in context: A332668 A206439 A097450 * A180682 A227426 A229950

Adjacent sequences:  A062300 A062301 A062302 * A062304 A062305 A062306

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 05 2001

STATUS

approved

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Last modified November 27 15:11 EST 2020. Contains 338683 sequences. (Running on oeis4.)