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 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 (list; graph; refs; listen; history; text; internal format)
 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=s-sum(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 (MIT/GNU Scheme) ;; with memoizing definec-macro: (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

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Last modified April 25 10:22 EDT 2024. Contains 371967 sequences. (Running on oeis4.)