id:A059451 - OEIS Search Results

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Number of ways n can be written as the sum of two numbers whose binary expansions have even numbers of zeros; also number of ways n can be written as the sum of two numbers whose binary expansions have odd numbers of zeros.

+0
1

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

	OFFSET	`1,8`
	COMMENT	`The only place where the two sequences differ is a(0) which is 1 for the odds and 0 for the evens.`
	LINKS	`IBM Ponder This, Feb. 2001`
	EXAMPLE	`a(16)=3 since 16=2+14=5+11=8+8 (in binary 10+1110=101+1011=1000+1000 where each term has an odd number of zeros) and since 16=1+15=4+12=7+9 (in binary 1+1111=100+1100=111+1001 where each term has an even number of zeros).`
	CROSSREFS	`Cf. A059009 and A059010 for the odd and even binary zeros sequences.` `Sequence in context: A156643 A128664 A003823 this_sequence A083817 A029273 A117963` `Adjacent sequences: A059448 A059449 A059450 this_sequence A059452 A059453 A059454`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Feb 02 2001`

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

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