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A256757 Number of iterations of A007733 required to reach 1. 4
0, 1, 2, 1, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 2, 1, 2, 3, 4, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 1, 3, 2, 3, 3, 4, 4, 3, 2, 3, 3, 4, 3, 3, 4, 5, 2, 4, 3, 2, 3, 4, 4, 3, 3, 4, 4, 5, 2, 3, 3, 3, 1, 3, 3, 4, 2, 4, 3, 4, 3, 4, 4, 3, 4, 3, 3, 4, 2, 5, 3, 4, 3, 2, 4, 4, 3, 4, 3, 3, 4, 3, 5, 4, 2, 3, 4, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

In other words, the minimal height (not counting k) of the power tower 2^(2^(...^(2^k)...)) required to make it eventually constant modulo n (=A245970(n)) for sufficiently large k.

a(n) <= A227944(n) + 1. - Max Alekseyev, Oct 11 2016

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

FORMULA

For n>1, a(n) = a(A007733(n)) + 1.

MATHEMATICA

A007733 = Function[n, MultiplicativeOrder[2, n/(2^IntegerExponent[n, 2])]];

a = Function[n, k = 0; m = n; While[m > 1, m = A007733[m]; k++]; k];

Table[a[n], {n, 100}] (* Ivan Neretin, Apr 13 2015 *)

PROG

(PARI) a(n) = {if (n==1, return(0)); nb = 1; while((n = znorder(Mod(2, n/2^valuation(n, 2)))) != 1, nb++); nb; } \\ Michel Marcus, Apr 11 2015

(Haskell)

a256757 n = fst $ until ((== 1) . snd)

            (\(i, x) -> (i + 1, fromIntegral $ a007733 x)) (0, n)

-- Reinhard Zumkeller, Apr 13 2015

CROSSREFS

Cf. A007733, A256607 (second iteration), A256758 (positions of records), A003434, A227944 (similarly built upon the totient function).

Sequence in context: A261787 A302480 A000374 * A277314 A120562 A178692

Adjacent sequences:  A256754 A256755 A256756 * A256758 A256759 A256760

KEYWORD

nonn,easy

AUTHOR

Ivan Neretin, Apr 09 2015

STATUS

approved

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)