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Search: id:A076092
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| A076092 |
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a(n)=n-2*sum(i=1,n,b(i)) (see comment for definition of b(i)). |
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2
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| 1, 0, -1, 0, 1, 2, 1, 0, -1, -2, -1, -2, -3, -2, -1, 0, -1, 0, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, 0, 1, 0, -1, -2, -3, -4, -5, -6, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 1, 0, -1, -2, -3, -4, -5, -4, -5, -4, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -4, -5, -4, -3
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Recall the modified Collatz map : x->x/2 if x is even; x->(3x+1)/2 if x is odd. Let C_m(n) denotes the image of n after m iterations. Then b(n)= (lim k ->infinity C_2k(n))-1 (from the Collatz conjecture C_2k(n) is constant = 1 or 2 for k sufficiently large).
Curiously the graph of a(n) has "regularities" around 0 and a pattern that becomes larger and larger when compared with a random sequence of the form n-2*sum(k=1,n,r(k)) where r(k) takes random values from (0;1).
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LINKS
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Paul Hanna, Graph of a(n) for n=1 up to 12000 .
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EXAMPLE
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b(12)=1 since, starting with 12 the Collatz map gives : 12->6->3->5->8->4->2->1, then C_6(12)=2 and then b(12) = C_6(12)-1 = 1
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PROGRAM
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(PARI) a(n)=n-2*sum(i=1, n, if(i<0, 0, s=i; c=0; while(s>1, s=(s%2)*(3*s+1)/2+(1-s%2)*s/2; c++); c)%2)
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CROSSREFS
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Cf. A076182 (b(n) sequence).
Adjacent sequences: A076089 A076090 A076091 this_sequence A076093 A076094 A076095
Sequence in context: A029359 A038698 A087991 this_sequence A080468 A080940 A080941
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KEYWORD
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sign
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 01 2002
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