A018908 Define sequence S(a_0,a_1) by a_{n+2} is least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 0. This is S(3,4).

3, 4, 6, 10, 17, 29, 50, 87, 152, 266, 466, 817, 1433, 2514, 4411, 7740, 13582, 23834, 41825, 73397, 128802, 226031, 396656, 696082, 1221538, 2143649, 3761841, 6601570, 11584947, 20330164, 35676950, 62608682, 109870577, 192809421, 338356946, 593775047

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, 4][n+1],
       1 +floor(a(n-1)^2/a(n-2)))
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, May 05 2014

Mathematica

a[n_] := a[n] = Switch[n, 0, 3, 1, 4, _, 1 + Floor[a[n-1]^2/a[n-2]]];
a /@ Range[0, 50] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A068922 A032408 A347567 * A353138 A052548 A232268

Adjacent sequences: A018905 A018906 A018907 * A018909 A018910 A018911

Keyword

nonn

Author

R. K. Guy

Status

approved