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A156055
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Define a map f by f(0) = f(1) = 0, otherwise f(k) = A087712(k); then a(n) is the number of steps for the trajectory of n under repeated iteration of f to "terminate".
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2
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1, 2, 3, 6, 4, 30, 7, 54, 3, 32, 5, 29, 31, 0, 3, 19, 8, 112, 55, 15, 27, 3, 3, 26, 1, 20, 223, 102, 33, 13, 6, 162, 1, 9, 10, 75, 30, 113, 21
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Here "terminate" means reaching 0 or a cycle.
Comments from M. F. Hasler, Feb 11 2009 (Start):
"Reaching a cycle" could be better defined: does it mean "reach a value that occured earlier" or "reach an element belonging to a cycle" ?
I think the second is the case, but the value 0 is currently listed at n=14, wouldn't it correspond to x=15 = least element of a nontrivial cycle ?
So would the offset be 2 ? or is there a missing term (since the first terms 1,2,3 seem well to correspond to x=1,2,3) ? (End)
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EXAMPLE
| a(4) = 6 because 4 -> [{2,2}->{1,1}] ->[{11}->{5}] -> [{5}->{3}] -> [{3}->{2}] -> [{2}->{1}] -> [{1}->{0}].
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MATHEMATICA
| f[n_] := FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n])]; g[n_] := Length@ NestWhileList[f, n, UnsameQ, All] - 2; Array[g, 39]
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CROSSREFS
| A variant of A098282, which is the official version of this sequence.
Cf. A087712.
Sequence in context: A119741 A126063 A137524 * A096357 A091507 A098282
Adjacent sequences: A156052 A156053 A156054 * A156056 A156057 A156058
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KEYWORD
| base,nonn,more
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 02 2009
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2009
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