

A053147


When cototient function (A051953) is iterated with initial value A002110(n), a(n) = value of first (largest) power of 2 which appears in the iteration.


0



2, 4, 8, 32, 32, 256, 32, 512, 256, 65536, 64, 512, 4096, 256, 512, 128, 16, 2048, 64, 64, 512, 8192, 256, 8192, 2048, 131072, 128, 8192, 1048576, 16, 2048, 2048, 32768, 8192, 512, 524288, 8192, 64, 16, 8192
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OFFSET

1,1


COMMENTS

In these iteration chains the number of non2powers seem to be dominant.
The sequence is not monotonic.


LINKS

Table of n, a(n) for n=1..40.


EXAMPLE

For n=10, the iteration chain of 43 terms is {6469693230, 5447823150, 4315810350, ..., 188416, 98304, 65536, 32768, ..., 4, 2, 1, 0} in which the largest power of 2 is 65536 = 2^16.
For n=11 the length is 61, including 54 numbers that are not powers of 2, and 7 powers of 2, of which the largest is 64 = a(11) < a(10) = 65536.


MATHEMATICA

Table[SelectFirst[NestWhileList[#  EulerPhi@ # &, P, # > 0 &], IntegerQ@ Log2@ # &], {P, FoldList[Times, Prime@ Range@ 30]}] (* Michael De Vlieger, Jun 11 2018 *)


CROSSREFS

Cf. A002110, A051953.
Sequence in context: A100083 A151406 A307611 * A128055 A061285 A194810
Adjacent sequences: A053144 A053145 A053146 * A053148 A053149 A053150


KEYWORD

more,nonn


AUTHOR

Labos Elemer, Feb 28 2000


EXTENSIONS

More terms from Michael De Vlieger, Jun 11 2018


STATUS

approved



