A018909 Define the sequence S(a_0,a_1) by a_{n+2} is the least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 0. This is S(3,6).

3, 6, 13, 29, 65, 146, 328, 737, 1657, 3726, 8379, 18843, 42375, 95295, 214305, 481942, 1083821, 2437364, 5481296, 12326680, 27721007, 62340730, 140195723, 315280889, 709023335, 1594495915, 3585801902, 8063975053, 18134770251, 40782602860, 91714461944

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

Index entries for Pisot sequences

Maple

a:= proc(n) option remember; `if`(n<2, [3, 6][n+1],
       1 +floor(a(n-1)^2/a(n-2)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, May 05 2014

Mathematica

a[n_] := a[n] = Switch[n, 0, 3, 1, 6, _, 1 + Floor[a[n-1]^2/a[n-2]]];
a /@ Range[0, 40] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A071014 A214260 A078061 * A093128 A005313 A213674

Adjacent sequences: A018906 A018907 A018908 * A018910 A018911 A018912

Keyword

nonn

Author

R. K. Guy

Status

approved