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A053039 Exponent of largest power of 2 which appears in the cototient-iteration started with n!. 3
0, 1, 2, 4, 5, 7, 9, 12, 14, 11, 13, 16, 14, 16, 23, 27, 23, 23, 24, 21, 23, 28, 42, 46, 26, 26, 26, 36, 43, 29, 50, 55, 37, 37, 40, 40, 39, 59, 39, 44, 68, 42, 42, 44, 51, 45, 50, 53, 49, 52, 51, 85, 55, 57, 53, 57, 60, 85, 62, 71, 62, 63, 60, 66, 66, 107, 67, 101, 76, 70, 75, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If the exponent is a(n), then the number of powers of 2 in the iteration-chain is 1+a(n), the maximal 2-power is 2^a(n) and the number of iterations (until fixed state) performed on these 2-powers is a(n).

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

For n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and starting the iteration of A051593 with n!, the first powers of 2 which appear are 1, 2, 4, 16, 32, 128, 512, 4096, 16384, 2048 and the corresponding exponents are a(n) = 0, 1, 2, 4, 5, 7, 9, 12, 14, 11.

MATHEMATICA

Log2 /@ Table[NestWhile[# - EulerPhi@ # &, n!, ! IntegerQ@ Log2@ # &], {n, 60}] (* Michael De Vlieger, Aug 15 2017 *)

PROG

(PARI) cototient(x)= x - eulerphi(x)

FunctionIterate(f, x, t)= {local(retval); retval = vector(0); while(x!=t, x = eval(concat(f, "(x)")); retval = concat(retval, x)); retval; }

A053039(x) = {local(li, fa, retval); count = 0; li = concat([x! ], FunctionIterate("cototient", x!, 0)); for(i=1, #li, fa = factor(li[i]); if(((matsize(fa)[1] == 1) && (fa[1, 1] == 2)), retval = fa[1, 2]; break)); retval}

for(i=1, 72, print1(A053039(i), ", ")) \\ Olaf Voß, Feb 21 2008

CROSSREFS

Cf. A051953, A053038, A053475.

Sequence in context: A007818 A158618 A000788 * A286753 A325543 A214051

Adjacent sequences:  A053036 A053037 A053038 * A053040 A053041 A053042

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 24 2000

EXTENSIONS

More terms from Olaf Voß, Feb 21 2008

STATUS

approved

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Last modified February 26 12:33 EST 2020. Contains 332279 sequences. (Running on oeis4.)