A328010 -id:A328010 - cp's OEIS frontend

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

Antoine Beaulieu, Oct 01 2019

See A328010 for further information.

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).

Cf. A259207, A328010.

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

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)

A028389 The 5x + 1 sequence beginning at 7.

Original entry on oeis.org

7, 36, 18, 9, 46, 23, 116, 58, 29, 146, 73, 366, 183, 916, 458, 229, 1146, 573, 2866, 1433, 7166, 3583, 17916, 8958, 4479, 22396, 11198, 5599, 27996, 13998, 6999, 34996, 17498, 8749, 43746, 21873, 109366, 54683, 273416, 136708, 68354, 34177, 170886, 85443, 427216

Offset: 0

N. J. A. Sloane, Dean Hickerson

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Cf. A259207, A328010, A328011.

f := proc(n) option remember; if n = 0 then 7 elif f(n-1) mod 2 = 0 then f(n-1)/2 else 5*f(n-1)+1; fi; end; seq(f(n), n=0..50);

a[0] = 7; a[n_] := a[n] = If[OddQ[a[n-1]], 5 a[n-1] + 1, a[n-1]/2];
a /@ Range[0, 50] (* Jean-François Alcover, Nov 03 2020 *)
NestList[If[OddQ[#],5#+1,#/2]&,7,50] (* Harvey P. Dale, Nov 03 2022 *)

a(0) = 7; a(n) = 5*a(n-1) + 1 if a(n-1) is odd, a(n) = a(n-1)/2 otherwise.

Named edited by Andrew Howroyd, Aug 21 2020

cp's OEIS Frontend

A328011 The 5x + 1 sequence beginning at 1.

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