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A037800 Number of occurrences of 01 in the binary expansion of n. 11
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,22

COMMENTS

Number of i such that d(i)>d(i-1), where Sum{d(i)*2^i: i=0,1,...,m} is base 2 representation of n.

This is the base-2 up-variation sequence; see A297330. - Clark Kimberling, Jan 18 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

Eric Weisstein's World of Mathematics, Digit Block.

Index entries for sequences related to binary expansion of n

FORMULA

a(2n) = a(n), a(2n+1) = a(n) + [n is even]. - Ralf Stephan, Aug 21 2003

G.f.: 1/(1-x) * sum(k>=0, t^5/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan, Sep 10 2003

a(n) = A069010(n) - 1, n>0. - Ralf Stephan, Sep 10 2003

PROG

(Haskell)

a037800 = f 0 . a030308_row where

   f c [_]          = c

   f c (1 : 0 : bs) = f (c + 1) bs

   f c (_ : bs)     = f c bs

-- Reinhard Zumkeller, Feb 20 2014

(PARI)

a(n) = { if(n == 0, 0, -1 + hammingweight(bitnegimply(n, n>>1))) };  \\ Gheorghe Coserea, Aug 31 2015

CROSSREFS

Cf. A014081, A014082, A033264, A056974, A056975, A056976, A056977, A056978, A056979, A056980.

Cf. A030308.

Sequence in context: A005590 A142598 A274372 * A144411 A138253 A261447

Adjacent sequences:  A037797 A037798 A037799 * A037801 A037802 A037803

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 18 13:01 EST 2019. Contains 319271 sequences. (Running on oeis4.)