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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.)