A256758 Position of first appearance of n in A256757.

1, 2, 3, 7, 19, 47, 163, 487, 1307, 2879, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 344373773, 688747547, 3486784401

Offset: 0

Author

Ivan Neretin, Apr 09 2015

Keywords

• nonn
• more

Comments

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.

Crossrefs

Cf. A007733, A007755 (similarly built upon the totient function), A173927 (similarly built upon the Carmichael lambda function), A256757.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a256758 = (+ 1) . fromJust . (`elemIndex`  a256757_list)
-- Reinhard Zumkeller, Apr 13 2015

Mathematica

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 *)

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

Extensions

a(15)-a(18) from Michel Marcus, Apr 11 2015

a(19)-a(21) from Amiram Eldar, Mar 04 2023