A328011 The 5x + 1 sequence beginning at 1.

1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1, 6, 3, 16, 8, 4, 2, 1

Offset

0,2

Comments

See A328010 for further information.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Alex V. Kontorovich & Jeffrey C. Lagarias, Stochastic Models for the 3x+1 and 5x+1 Problems, arXiv:0910.1944 [math.NT], 2009.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Formula

a(n+1) = 5*a(n) + 1 if a(n) is odd, a(n+1) = a(n)/2 otherwise.

From Colin Barker, Oct 08 2019: (Start)

G.f.: (1 + 6*x + 3*x^2 + 16*x^3 + 8*x^4 + 4*x^5 + 2*x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = a(n-7) for n>6.

(End)

Prog

(PARI) Vec((1 + 6*x + 3*x^2 + 16*x^3 + 8*x^4 + 4*x^5 + 2*x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^80)) \\ Colin Barker, Oct 08 2019

Crossrefs

Cf. A259207, A328010.

Sequence in context: A248267 A236415 A267831 * A231881 A229005 A067990

Adjacent sequences: A328008 A328009 A328010 * A328012 A328013 A328014

Keyword

nonn,easy

Author

Antoine Beaulieu, Oct 01 2019

Status

approved