A166396 - OEIS

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

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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: A262666 A124737 A121303 * A152221 A144092 A333467

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