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Search: id:A071542
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| A071542 |
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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). |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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FORMULA
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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...)
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EXAMPLE
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17 (= 10001 in binary) -> 15 (= 1111) -> 11 (= 1011) -> 8 (= 1000) -> 7 (= 111) -> 4 (= 100) -> 3 (= 11) -> 1 -> 0 hence a(17)=8
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PROGRAM
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(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, ", "); ); )
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CROSSREFS
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Sequence in context: A062108 A100682 A075355 this_sequence A088461 A135020 A034888
Adjacent sequences: A071539 A071540 A071541 this_sequence A071543 A071544 A071545
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 02 2002
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