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A037809 Number of i such that d(i)<=d(i-1), where Sum{d(i)*2^i: i=0,1,...,m} is the base 2 representation of n. 2
0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 5, 5, 5, 4, 5, 4, 4, 4, 5, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 3, 4, 3, 3, 3, 4, 4, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..90.

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

R. Stephan, Table of generating functions

FORMULA

G.f. -1/(1-x) + 1/(1-x) * sum(k>=0, (t+t^3+t^4)/(1+t+t^2+t^3), t=x^2^k). a(n) = A056973(n) + A000120(n) - 1. a(n) = b(n)-1, with b(0)=0, b(2n)=b(n)+[n even], b(2n+1)=b(n)+1. - Ralf Stephan, Oct 05 2003

EXAMPLE

The base-2 representation of n=4 is 100 with d(0)=0, d(1)=0, d(2)=1. There is one fall-or-equal from d(0) to d(1), so a(4)=1. - R. J. Mathar, Oct 16 2015

MAPLE

A037809 := proc(n)

    a := 0 ;

    dgs := convert(n, base, 2);

    for i from 2 to nops(dgs) do

        if op(i, dgs)<=op(i-1, dgs) then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Oct 16 2015

CROSSREFS

Cf. A033265.

Sequence in context: A122922 A278570 A046799 * A280534 A129451 A097195

Adjacent sequences:  A037806 A037807 A037808 * A037810 A037811 A037812

KEYWORD

nonn,base

AUTHOR

Clark Kimberling

EXTENSIONS

Sign in Name corrected. - R. J. Mathar, Oct 16 2015

STATUS

approved

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)