A285099 a(n) is the zero-based index of the second least significant 1-bit in the base-2 representation of n, or 0 if there are fewer than two 1-bits in n.

0, 0, 0, 1, 0, 2, 2, 1, 0, 3, 3, 1, 3, 2, 2, 1, 0, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 0, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 0, 6, 6, 1, 6, 2, 2, 1, 6, 3, 3, 1, 3, 2, 2, 1, 6, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1, 6, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

If A000120(n) < 2, a(n) = 0, otherwise a(n) = A007814(A129760(n)) = A007814(n AND (n-1)). [Where AND is bitwise-and, A004198].

From Jeffrey Shallit, Apr 19 2020: (Start)

This is a 2-regular sequence, satisfying the identities

a(4n) = -a(n) + a(2n),

a(4n+2) = a(4n+1),

a(8n+1) = -a(2n+1) + 2a(4n+1),

a(8n+3) = a(4n+3),

a(8n+5) = 2a(4n+3),

a(8n+7) = a(4n+3). (End)

Example

For n = 3, "11" in binary, the second least significant 1-bit (the second 1-bit from the right) is at position 1 (when the rightmost position is position 0), thus a(3) = 1.
For n = 4, "100" in binary, there is just one 1-bit present, thus a(4) = 0.
For n = 5, "101" in binary, the second 1-bit from the right is at position 2, thus a(5) = 2.
For n = 25, "11001" in binary, the second 1-bit from the right is at position 3, thus a(25) = 3.

Mathematica

a007814[n_]:=IntegerExponent[n, 2]; a[n_]:=If[DigitCount[n, 2, 1]<2, 0, a007814[BitAnd[n, n - 1]]]; Table[a[n], {n, 0, 150}] (* Indranil Ghosh, Apr 20 2017 *)

Prog

(Scheme) (define (A285099 n) (if (<= (A000120 n) 1) 0 (A007814 (A004198bi n (- n 1))))) ;; A004198bi implements bitwise-and.
(Python)
import math
def a007814(n): return int(math.log(n - (n & n - 1), 2))
def a(n): return 0 if bin(n)[2:].count("1") < 2 else a007814(n & (n - 1)) # Indranil Ghosh, Apr 20 2017

Crossrefs

Cf. A000120, A004198, A007814, A129760, A285097.

Sequence in context: A146527 A352556 A368282 * A306754 A063250 A348967

Adjacent sequences: A285096 A285097 A285098 * A285100 A285101 A285102

Keyword

nonn,base

Author

Antti Karttunen, Apr 19 2017

Status

approved