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 A033265 Number of i such that d(i) >= d(i-1), where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n. 7
 0, 1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 4, 4, 5, 4, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 5, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 6, 5, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 5, 4, 5, 5, 5, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Ralf Stephan, Some divide-and-conquer sequences ... Ralf Stephan, Table of generating functions FORMULA From Ralf Stephan, Oct 05 2003: (Start) a(0) = 0, a(2n) = a(n) + 1, a(2n+1) = a(n) + [n odd]. a(n) = A014081(n) + A023416(n). G.f. 1/(1-x) * Sum_{k>=0} (t^2 + t^3 + t^4)/((1+t)*(1+t^2)), t=x^2^k). (End) a(n) = -1 + A297113(A005940(1+n)). - Antti Karttunen, Dec 30 2017 EXAMPLE The base-2 representation of n=4 is 100 with d(0)=0, d(1)=0, d(2)=1. There are two rise-or-equal, one from d(0) to d(1) and one from d(1) to d(2), so a(4)=2. - R. J. Mathar, Oct 16 2015 MAPLE A033265 := 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. A014081, A023416, A037800, A037809, A005940, A156552, A297113. Sequence in context: A334098 A263922 A057526 * A096004 A193495 A071068 Adjacent sequences:  A033262 A033263 A033264 * A033266 A033267 A033268 KEYWORD nonn,base AUTHOR EXTENSIONS Sign in Name corrected by R. J. Mathar, Oct 16 2015 STATUS approved

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Last modified September 19 05:46 EDT 2021. Contains 347551 sequences. (Running on oeis4.)