A166396 - OEIS

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A166396

a(n) = the number of distinct positive decimal values k of substrings in the binary representation of n where k+1 is also the value of at least one substring in the binary representation of n.

0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 2, 3, 3, 3, 0, 1, 1, 1, 3, 2, 1, 3, 2, 3, 3, 3, 3, 4, 5, 4, 0, 1, 1, 1, 3, 1, 2, 3, 3, 2, 3, 1, 3, 6, 3, 4, 2, 3, 3, 3, 3, 5, 3, 3, 4, 5, 4, 5, 5, 5, 7, 5, 0, 1, 1, 1, 3, 1, 2, 3, 4, 2, 1, 3, 4, 3, 5, 4, 3, 2, 2, 3, 6, 3, 1, 5, 3, 6, 6, 4, 3, 7, 5, 5, 2, 3, 3, 3, 3, 3, 5, 3, 4, 5, 6 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,6`
	COMMENTS	`A166395(n) = A166396(n) + 1 if n is not of the form 2^m -1. A166395(2^m -1) = A166396(2^m -1) = 0, for all m.`
	LINKS	`Table of n, a(n) for n=1..105.`
	EXAMPLE	`13 in binary is 1101. 1 and 10 (2 in decimal) both occur as substrings in 1101. 10 and 11 (3 in decimal) both occur as substrings. And 101 (5 in decimal) and 110 (6 in decimal) both occur as substrings. Since there are three positive values k where both binary k and binary k+1 also occurs as a substring in 1101, then a(13) = 3.`
	CROSSREFS	`Cf. A166395` `Sequence in context: A135549 A124737 A121303 * A152221 A144092 A120648` `Adjacent sequences: A166393 A166394 A166395 * A166397 A166398 A166399`
	KEYWORD	`base,nonn`
	AUTHOR	`Leroy Quet, Oct 13 2009`
	EXTENSIONS	`More terms from Sean A. Irvine, Mar 02 2010`
	STATUS	`approved`

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Last modified May 23 22:33 EDT 2013. Contains 225613 sequences.