

A156055


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".


2



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
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OFFSET

1,2


COMMENTS

Here "terminate" means reaching 0 or a cycle.
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)


LINKS

Table of n, a(n) for n=1..39.


EXAMPLE

a(4) = 6 because 4 > [{2,2}>{1,1}] >[{11}>{5}] > [{5}>{3}] > [{3}>{2}] > [{2}>{1}] > [{1}>{0}].


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]


CROSSREFS

A variant of A098282, which is the official version of this sequence.
Cf. A087712.
Sequence in context: A229774 A137524 A282507 * A096357 A091507 A098282
Adjacent sequences: A156052 A156053 A156054 * A156056 A156057 A156058


KEYWORD

base,nonn,more


AUTHOR

Robert G. Wilson v, Feb 02 2009


EXTENSIONS

Edited by N. J. A. Sloane, Feb 10 2009


STATUS

approved



