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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In these iteration chains the number of non-2-powers 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

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Last modified January 20 20:50 EST 2021. Contains 340332 sequences. (Running on oeis4.)