id:A062602 - OEIS Search Results

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Number of ways of writing n = p+c with p prime and c nonprime (1 or a composite number).

+0
8

0, 0, 1, 1, 0, 2, 1, 2, 2, 1, 4, 3, 3, 3, 4, 2, 6, 3, 5, 4, 6, 3, 8, 3, 7, 4, 9, 5, 9, 4, 8, 7, 9, 4, 11, 3, 11, 9, 10, 6, 12, 5, 11, 8, 12, 7, 14, 5, 13, 7, 15, 9, 15, 6, 14, 10, 16, 9, 16, 5, 15, 13, 16, 8, 18, 6, 18, 15, 17, 9, 19, 8, 18, 12, 19, 11, 21, 7, 21, 14, 20, 13, 22, 7, 21, 14 (list; graph; listen)

	OFFSET	`1,6`
	LINKS	`Index entries for sequences related to Goldbach conjecture`
	FORMULA	`a(n+1) = SUM(A010051(k)*A005171(n-k+1): 1<=k<=n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 05 2009]`
	EXAMPLE	`n = 22 has Floor[n/2] = 11 partitions of form n = a+b; 3 partitions are of prime+prime [3+19 = 5+17 = 11+11], 3 partitions are of prime+nonprime [2+20 = 7+15 = 13+9], 5 partitions are nonprime+nonprime [1+21 = 4+18 = 6+16 = 8+14 = 10+12]. So a(22) = 3.`
	CROSSREFS	`Cf. A061358, A014092, A062610.` `Sequence in context: A035436 A035369 A129719 this_sequence A123148 A166548 A134997` `Adjacent sequences: A062599 A062600 A062601 this_sequence A062603 A062604 A062605`
	KEYWORD	`nonn,new`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Jul 04 2001`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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