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A256758
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Position of first appearance of n in A256757.
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2
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1, 2, 3, 7, 19, 47, 163, 487, 1307, 2879, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 344373773, 688747547, 3486784401
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OFFSET
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0,2
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COMMENTS
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Smallest number m such that the trajectory of m under iteration of A007733 takes n steps to reach the fixed point.
The terms a(1)..a(9) are primes. The next eight terms are powers of 3, so that for n=10..17, a(n)=3^(n-1), but this apparently established pattern breaks at a(18), which is again a prime.
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LINKS
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MATHEMATICA
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A007733 = Function[n, MultiplicativeOrder[2, n/(2^IntegerExponent[n, 2])]];
A256757 = Function[n, k = 0; m = n; While[m > 1, m = A007733[m]; k++]; k];
a = Function[n, t = 1; While[A256757[t] < n , t++]; t]; Table[a[n], {n, 0, 9}] (* Ivan Neretin, Apr 13 2015 *)
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PROG
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(PARI) a007733(n) = znorder(Mod(2, n/2^valuation(n, 2)));
a256757(n) = {if (n==1, return(0)); nb = 1; while((n = a007733(n)) != 1, nb++); nb; }
a(n) = {k = 1; while(a256757(k) != n, k++); k; } \\ Michel Marcus, Apr 11 2015
(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a256758 = (+ 1) . fromJust . (`elemIndex` a256757_list)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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