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A334040
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Number of odd numbers larger than n in the Collatz trajectory of n.
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1
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0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 2, 0, 0, 1, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 38, 0, 0, 2, 36, 0, 0, 0, 1, 0, 0, 0, 4, 0, 35, 0, 2, 0, 0, 1, 34, 0, 0, 0, 1, 0, 0, 33, 35, 0, 1, 0, 3, 0, 0, 32, 33, 0, 0, 0, 1, 0, 0, 0, 31, 0, 33, 0, 2, 0, 0, 2, 4, 0, 0, 31, 32
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OFFSET
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1,7
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LINKS
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EXAMPLE
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For n=7 the Collatz process is: 7,22,(11),34,(17),52,26,(13),40,20,10,5,16,8,4,2,1. The numbers in the parentheses are odd numbers in the Collatz process for n=7 that are bigger than 7. There are three of them, hence a(7)=3.
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MATHEMATICA
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Table[Count[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&], _?(#>n&&OddQ[#]&)], {n, 90}] (* Harvey P. Dale, Aug 03 2023 *)
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PROG
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(PARI) f(n) = if (n%2, 3*n+1, n/2);
a(n) = {my(nb = 0, m=n); while ((n=f(n)) != 1, if ((n % 2) && (n>m), nb++)); nb; } \\ Michel Marcus, Jun 01 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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