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

Offset: 1

Author

Labos Elemer, Feb 28 2000

Keywords

• nonn
• more

Comments

In these iteration chains the number of non-2-powers seem to be dominant.

The sequence is not monotonic.

Examples

			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.
		

Crossrefs

Cf. A002110, A051953.

Programs

Mathematica

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

Extensions

More terms from Michael De Vlieger, Jun 11 2018

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