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%I #18 Dec 21 2023 07:43:23
%S 0,3,1,2,9,5,8,6,18,12,10,4,27,7,17,15,36,21,19,11,45,14,26,24,54,30,
%T 28,13,63,16,35,33,72,39,37,20,81,23,44,42,90,48,46,22,99,25,53,51,
%U 108,57,55,29,117,32,62,60,126,66,64,31,135,34,71,69,144,75,73,38,153,41,80
%N Inverse of permutation in A074307.
%C A permutation of the nonnegative integers.
%H G. Venturini, <a href="https://doi.org/10.1002/sapm1992863185">Iterates of number-theoretic functions with periodic rational coefficients (Generalization of the 3x+1 problem)</a>, Stud. Appl. Math., 86 (1992), 185-218.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1).
%F a(A074307(n)) = n. - _R. J. Mathar_, Feb 27 2007
%p A074305 := proc(n) option remember ; local m ; m := floor(n/3) ; if 3*m = n then 2*m ; elif 3*m+1 =n then 4*m+3 ; else 4*m+1 ; fi ; end: A074307 := proc(n) A074305(A074305(n)) ; end: A074308 := proc(n) local a ; a := 0 ; while A074307(a) <> n do a := a+1 ; od ; RETURN(a) ; end: for n from 0 to 70 do printf("%d, ",A074308(n)) ; od ; # _R. J. Mathar_, Feb 27 2007
%t A074305[n_] := A074305[n] = Module[{m = Floor[n/3]}, If[3m == n, 2m, If[3m + 1 == n, 4m + 3, 4m + 1]]];
%t A074307[n_] := A074305[A074305[n]];
%t A074308[n_] := A074308[n] = Module[{a = 0}, While[A074307[a] != n, a = a+1]; Return[a]];
%t Table[A074308[n], {n, 0, 70}] (* _Jean-François Alcover_, Dec 21 2023, after _R. J. Mathar_ *)
%Y Cf. A074305, A074306, A074307.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Sep 23 2002
%E Corrected and extended by _R. J. Mathar_, Feb 27 2007
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