A256758 - OEIS

%I #39 Mar 04 2023 05:01:18

%S 1,2,3,7,19,47,163,487,1307,2879,19683,59049,177147,531441,1594323,

%T 4782969,14348907,43046721,86093443,344373773,688747547,3486784401

%N Position of first appearance of n in A256757.

%C Smallest number m such that the trajectory of m under iteration of A007733 takes n steps to reach the fixed point.

%C 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.

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

%t A256757 = Function[n, k = 0; m = n; While[m > 1, m = A007733[m]; k++]; k];

%t a = Function[n, t = 1; While[A256757[t] < n , t++]; t]; Table[a[n], {n, 0, 9}] (* _Ivan Neretin_, Apr 13 2015 *)

%o (PARI) a007733(n) = znorder(Mod(2, n/2^valuation(n, 2)));

%o a256757(n) = {if (n==1, return(0)); nb = 1; while((n = a007733(n)) != 1, nb++); nb; }

%o a(n) = {k = 1; while(a256757(k) != n, k++); k;} \\ _Michel Marcus_, Apr 11 2015

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a256758 = (+ 1) . fromJust . (`elemIndex`  a256757_list)

%o -- _Reinhard Zumkeller_, Apr 13 2015

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

%K nonn,more

%O 0,2

%A _Ivan Neretin_, Apr 09 2015

%E a(15)-a(18) from _Michel Marcus_, Apr 11 2015

%E a(19)-a(21) from _Amiram Eldar_, Mar 04 2023