A033478 3x+1 sequence beginning at 3.

3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1

Offset: 0

Author

Jeff Burch

Keywords

• nonn
• easy

References

• C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 374.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Row 3 of A347270.

Programs

Maple

f:=proc(n) if n mod 2 = 0 then n/2 else 3*n+1; fi; end; g:=proc(n) local i,t1; t1:=[n]; for i from 1 to 120 do t1:=[op(t1),f(t1[nops(t1)])]; od; t1; end; g(3);

Mathematica

A033478list[nmax_]:=PadRight[{3,10,5,16,8},nmax+1,{2,1,4}];A033478list[100] (* Paolo Xausa, May 31 2023 *)

PARI

a(n)=if(n>4,[2,1,4][n%3+1],[3,10,5,16,8][n+1]) \\ Charles R Greathouse IV, Jun 22 2016

PARI

Vec((3 + 10*x + 5*x^2 + 13*x^3 - 2*x^4 - x^5 - 14*x^6 - 7*x^7) / ((1 - x)*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Oct 04 2019

Formula

From Colin Barker, Oct 04 2019: (Start)

G.f.: (3 + 10*x + 5*x^2 + 13*x^3 - 2*x^4 - x^5 - 14*x^6 - 7*x^7) / ((1 - x)*(1 + x + x^2)).

a(n) = a(n-3) for n>7.

(End)