A156055 - OEIS

%I #7 Jun 17 2015 08:24:21

%S 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,

%T 102,33,13,6,162,1,9,10,75,30,113,21

%N 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".

%C Here "terminate" means reaching 0 or a cycle.

%C From _M. F. Hasler_, Feb 11 2009: (Start)

%C "Reaching a cycle" could be better defined: does it mean "reach a value that occured earlier" or "reach an element belonging to a cycle"?

%C 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?

%C 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)

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

%t f[n_] := FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n])]; g[n_] := Length@ NestWhileList[f, n, UnsameQ, All] - 2; Array[g, 39]

%Y A variant of A098282, which is the official version of this sequence.

%Y Cf. A087712.

%K base,nonn,more

%O 1,2

%A _Robert G. Wilson v_, Feb 02 2009

%E Edited by _N. J. A. Sloane_, Feb 10 2009