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A075476
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Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+7. Corresponds to selection of every 16th term from A074474.
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10
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12, 84, 12, 14, 12, 35, 12, 14, 12, 17, 12, 14, 12, 25, 12, 14, 12, 25, 12, 14, 12, 27, 12, 14, 12, 17, 12, 14, 12, 38, 12, 14, 12, 25, 12, 14, 12, 45, 12, 14, 12, 17, 12, 14, 12, 27, 12, 14, 12, 20, 12, 14, 12, 79, 12, 14, 12, 17, 12, 14, 12, 20, 12, 14, 12, 33, 12, 14, 12
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OFFSET
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0,1
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COMMENTS
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Remark that initial values of form 64m+r, if r={3, 11, 19, 27, 35, 43, 51, 55} provide first-sink-lengths {7, 9, 7, 9, 7, 9, 7, 9} respectively; e.g. {64k+19, 192k+58, 96k+29, 288k+88, 144k+44, 72k+22, 36k+11} submerge first below initial value at the 7th term, 36k+11<64k+19.
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LINKS
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FORMULA
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a(n) = A074473(64n+7), n=0, ..., 256
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EXAMPLE
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n=0: 64n+7=7, list={7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5..}, i.e. the 12th term is the first that <12, the initial value.
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MATHEMATICA
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lcoll[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # >= n &]]; Table[lcoll[64*i + 7], {i, 0, 68}] (* Jayanta Basu, Jun 15 2013 *)
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PROG
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(PARI)
A074473(n) = if(1==n, n, my(org_n=n); for(i=1, oo, if(n<org_n, return(i)); n = A006370(n)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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