A053147 - OEIS

A053147

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

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, 16, 16, 256, 16

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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..44.

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

nonn,more

AUTHOR

Labos Elemer, Feb 28 2000

EXTENSIONS

More terms from Michael De Vlieger, Jun 11 2018

a(41)-a(44) from Jinyuan Wang, Jul 12 2021

STATUS

approved