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

Author

R. K. Guy

Keywords

• nonn

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

Programs

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 *)