A074308 Inverse of permutation in A074307.

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, 28, 13, 63, 16, 35, 33, 72, 39, 37, 20, 81, 23, 44, 42, 90, 48, 46, 22, 99, 25, 53, 51, 108, 57, 55, 29, 117, 32, 62, 60, 126, 66, 64, 31, 135, 34, 71, 69, 144, 75, 73, 38, 153, 41, 80

Offset

0,2

Comments

A permutation of the nonnegative integers.

Links

Table of n, a(n) for n=0..70.

G. Venturini, Iterates of number-theoretic functions with periodic rational coefficients (Generalization of the 3x+1 problem), Stud. Appl. Math., Vol. 86 (1992), pp. 185-218.

Index entries for sequences that are permutations of the natural numbers.

Index entries for linear recurrences with constant coefficients, 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).

Formula

a(A074307(n)) = n. - R. J. Mathar, Feb 27 2007

From Elmo R. Oliveira, May 15 2026: (Start)

a(n) = a(n-8) + a(n-16) - a(n-24).

G.f.: x*(3 + x + 2*x^2 + 9*x^3 + 5*x^4 + 8*x^5 + 6*x^6 + 18*x^7 + 9*x^8 + 9*x^9 + 2*x^10 + 18*x^11 + 2*x^12 + 9*x^13 + 9*x^14 + 18*x^15 + 6*x^16 + 8*x^17 + 5*x^18 + 9*x^19 + 2*x^20 + x^21 + 3*x^22) / ((1 - x^8)*(1 - x^16)). (End)

Maple

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

Mathematica

A074305[n_] := A074305[n] = Module[{m = Floor[n/3]}, If[3m == n, 2m, If[3m + 1 == n, 4m + 3, 4m + 1]]];
A074307[n_] := A074305[A074305[n]];
A074308[n_] := A074308[n] = Module[{a = 0}, While[A074307[a] != n, a = a+1]; Return[a]];
Table[A074308[n], {n, 0, 70}] (* Jean-François Alcover, Dec 21 2023, after R. J. Mathar *)

Crossrefs

Cf. A074305, A074306, A074307.

Sequence in context: A152252 A152229 A238388 * A237186 A058142 A058144

Adjacent sequences: A074305 A074306 A074307 * A074309 A074310 A074311

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 23 2002

Extensions

Corrected and extended by R. J. Mathar, Feb 27 2007

Status

approved