id:A141097 - OEIS Search Results

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Number of unordered pairs of coprime composite numbers that sum to 2n.

+0
5

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 1, 3, 0, 1, 0, 0, 3, 3, 0, 0, 3, 0, 3, 2, 0, 3, 4, 0, 1, 2, 1, 4, 5, 0, 0, 3, 1, 5, 5, 0, 4, 6, 0, 5, 2, 0, 7, 6, 0, 0, 9, 2, 8, 8, 0, 6, 4, 1, 8, 4, 1, 9, 9, 1, 4, 10, 2, 8, 11, 0, 3, 11, 3, 10, 4, 2, 12, 8, 1, 4, 13, 2 (list; graph; listen)

	OFFSET	`1,29`
	COMMENT	`See A141095 for pairs of coprime nonprime numbers. It appears that a(n) > 0 except for the 43 values of 2n given in A141098. Roberts says that A. M. Vaidya proved that a(n) > 0 for all sufficiently large n.`
	REFERENCES	`Joe Roberts, "Lure of the Integers", The Mathematical Association of America, 1992, p. 190.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..10000` `Carlos Rivera, Conjecture 33: The Goldbach Temptation`
	EXAMPLE	`a(17)=1 because 34 = 9+25.`
	MATHEMATICA	`Table[cnt=0; Do[If[GCD[2n-i, i]==1 && !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i, 3, n, 2}]; cnt, {n, 100}]`
	CROSSREFS	`Cf. A141099, A141100.` `Sequence in context: A132213 A154312 A119900 this_sequence A096335 A129503 A144185` `Adjacent sequences: A141094 A141095 A141096 this_sequence A141098 A141099 A141100`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jun 02 2008`

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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.

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