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

0,1

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).

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)

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 *)

Prog

(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

Crossrefs

Row 3 of A347270.

Sequence in context: A247034 A275511 A035411 * A285576 A246777 A111127

Adjacent sequences: A033475 A033476 A033477 * A033479 A033480 A033481

Keyword

nonn,easy

Author

Jeff Burch

Status

approved