A081743 - OEIS

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A081743

a(1)=1 then a(n)=a(n/2^k)+1 if n is even and 2^k is the largest power of 2 dividing n, a(n)=a(n-1) otherwise.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000120(n) + A059841(n). - Robert Israel, Sep 09 2020

MAPLE

a:= proc(n) option remember;

if n::even then 1+procname(n/2^padic:-ordp(n, 2)) else procname(n-1) fi

end proc:

a(1):= 1:

map(a, [$1..200]); # Robert Israel, Sep 09 2020

MATHEMATICA

Nest[Append[#1, If[EvenQ@ #2, 1 + #1[[#2/2^IntegerExponent[#2, 2]]], #1[[-1]] ]] & @@ {#, Length@ # + 1} &, {1}, 104] (* Michael De Vlieger, Sep 09 2020 *)

PROG

(PARI) a(n)=if(n<2, 1, if(n%2, a(n-1), a(n/2^valuation(n, 2))+1))

CROSSREFS

Cf. A000120, A059841.

Sequence in context: A347387 A196046 A152724 * A247069 A367008 A366800

Adjacent sequences: A081740 A081741 A081742 * A081744 A081745 A081746

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 07 2003

STATUS

approved