id:A073750 - OEIS Search Results

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Factors of 2 in the denominators of the fractional coefficients of the square-root of the prime power series: sum_{n=0..inf} p_n x^n, where p_n is the n-th prime and p_0 is defined to be 1.

+0
2

0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 4, 4, 7, 7, 7, 8, 8, 8, 10, 10, 10, 11, 11, 11, 15, 15, 15, 16, 16, 16, 18, 18, 18, 19, 19, 19, 22, 22, 22, 23, 23, 23, 25, 25, 25, 26, 26, 26, 31, 31, 31, 32, 32, 32, 34, 34, 34, 35, 35, 35, 38, 38, 38, 39, 39, 39, 41, 41, 41, 42, 42, 42 (list; graph; listen)

	OFFSET	`0,7`
	COMMENT	`Are all the denominators exact powers of 2?`
	FORMULA	`Convolution of sum_{n=0..inf} A073749(n)/[D_n*2^{a(n)}] x^n yields the prime power series sum_{n=0..inf} p_n x^n, where p_n is the n-th prime and p_0=1 and where D_n is a positive integer; D_n for the first 60 terms is 1 (is it always equal to 1?).`
	CROSSREFS	`Cf. A073749.` `Sequence in context: A096056 A050501 A105590 this_sequence A120204 A156349 A069941` `Adjacent sequences: A073747 A073748 A073749 this_sequence A073751 A073752 A073753`
	KEYWORD	`easy,frac,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Aug 07 2002`

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

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