A106151 - OEIS

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A106151

In binary representation of n: delete one zero in each contiguous block of zeros.

1, 1, 3, 2, 3, 3, 7, 4, 5, 3, 7, 6, 7, 7, 15, 8, 9, 5, 11, 6, 7, 7, 15, 12, 13, 7, 15, 14, 15, 15, 31, 16, 17, 9, 19, 10, 11, 11, 23, 12, 13, 7, 15, 14, 15, 15, 31, 24, 25, 13, 27, 14, 15, 15, 31, 28, 29, 15, 31, 30, 31, 31, 63, 32, 33, 17, 35, 18, 19, 19, 39, 20, 21, 11, 23, 22, 23 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`a(n) <= n; a(n) = n iff n = 2^k-1: a(A000225(n))=A000225(n);` `A000120(a(n))=A000120(n); A023416(a(n))=A023416(n)-A087116(n).`
	LINKS	`Index entries for sequences related to binary expansion of n`
	FORMULA	`a(n) = b(n, 0), where b(n, r) = if n = 1 then 1 else b(floor(n/2), 1 - n mod 2)*(1 + floor((1 + r + n mod 2)/2)) + n mod 2.`
	EXAMPLE	`n=144 = '10010000' -> '101000' = 40 = a(144);` `n=145 = '10010001' -> '101001' = 41 = a(145);` `n=146 = '10010010' -> '10101' = 21 = a(146).`
	CROSSREFS	`Cf. A007088, A038573, A090078.` `Sequence in context: A087713 A089319 A117231 * A007888 A188723 A077178` `Adjacent sequences: A106148 A106149 A106150 * A106152 A106153 A106154`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 07 2005`

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Last modified February 14 17:10 EST 2012. Contains 205644 sequences.