

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).


24



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

Antti Karttunen, Table of n, a(n) for n = 0..131072


FORMULA

a(0)=0, a(n) = 1 + A071542(n  A000120(n)).  Antti Karttunen, Oct 24 2012
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, ", "); ); )
(PARI) a(n)=my(k); while(n, n=hammingweight(n); k++); k \\ Charles R Greathouse IV, Oct 30 2012
(GNU/MIT Scheme with memoizing definecmacro): (definec (A071542 n) (if (zero? n) n (+ 1 (A071542 ( n (A000120 n)))))) ;; Antti Karttunen, Oct 24 2012


CROSSREFS

Cf. A000120, A011371, A071542, A213706, A213707, A213708, A218254.
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).
Sequence in context: A274618 A176843 A238263 * A264810 A176841 A176814
Adjacent sequences: A071539 A071540 A071541 * A071543 A071544 A071545


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jun 02 2002


EXTENSIONS

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


STATUS

approved



