

A071542


Number of steps to reach 0 starting with n and using the iterated process : x > x  (number of 1's in binary representation of x).


25



0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25
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OFFSET

0,3


LINKS



FORMULA

It seems that a(n) ~ C n/log(n) asymptotically with C = 1.4... (n = 10^6 gives C = 1.469..., n = 10^7 gives C = 1.4614...).


EXAMPLE

17 (= 10001 in binary) > 15 (= 1111) > 11 (= 1011) > 8 (= 1000) > 7 (= 111) > 4 (= 100) > 3 (= 11) > 1 > 0, hence a(17)=8.


MATHEMATICA

Table[1 + Length@ NestWhileList[#  DigitCount[#, 2, 1] &, n, # > 0 &], {n, 0, 75}] (* Michael De Vlieger, Jul 16 2017 *)


PROG

(PARI) for(n=1, 150, s=n; t=0; while(s!=0, t++; s=ssum(i=1, length(binary(s)), component(binary(s), i))); if(s==0, print1(t, ", "); ); )
(MIT/GNU Scheme)
;; with memoizing definecmacro:


CROSSREFS

A179016 gives the unique infinite sequence whose successive terms are related by this iterated process (in reverse order). Also, it seems that for n>=0, a(A213708(n) = a(A179016(n+1)) = n.
A213709(n) = a((2^(n+1))1)  a((2^n)1).


KEYWORD

easy,nonn


AUTHOR



EXTENSIONS

Starting offset changed to 0 with a(0) prepended as 0 by Antti Karttunen, Oct 24 2012


STATUS

approved



