A166395 a(n) = the number of distinct nonnegative 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, 2, 0, 2, 2, 3, 0, 2, 2, 2, 3, 4, 4, 4, 0, 2, 2, 2, 4, 3, 2, 4, 3, 4, 4, 4, 4, 5, 6, 5, 0, 2, 2, 2, 4, 2, 3, 4, 4, 3, 4, 2, 4, 7, 4, 5, 3, 4, 4, 4, 4, 6, 4, 4, 5, 6, 5, 6, 6, 6, 8, 6, 0, 2, 2, 2, 4, 2, 3, 4, 5, 3, 2, 4, 5, 4, 6, 5, 4, 3, 3, 4, 7, 4, 2, 6, 4, 7, 7, 5, 4, 8, 6, 6, 3, 4, 4, 4, 4, 4, 6, 4, 5, 6, 7

Offset

1,2

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. 0 and 1 both occur as substrings in 1101. 1 and 10 (2 in decimal) both occur as substrings. 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 four values k where both binary k and binary k+1 also occurs as a substring in 1101, then a(13) = 4.

Crossrefs

Cf. A166396

Sequence in context: A339434 A348325 A103863 * A061199 A352128 A334203

Adjacent sequences: A166392 A166393 A166394 * A166396 A166397 A166398

Keyword

base,nonn

Author

Leroy Quet, Oct 13 2009

Extensions

Definition corrected by Sean A. Irvine, Mar 02 2010

More terms from Sean A. Irvine, Mar 02 2010

Status

approved