A019477 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(3,15) (agrees with A019478 only for n <= 23).

3, 15, 76, 386, 1961, 9963, 50618, 257170, 1306579, 6638211, 33726124, 171349094, 870556961, 4422955527, 22471287314, 114167721214, 580041026803, 2946958993287, 14972332829596, 76068500060858, 386473956154025, 1963521282342195, 9975874867682426

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, 15][n+1], floor(a(n-1)^2/a(n-2))+1)
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Sep 18 2015

Mathematica

S[a_, b_, n_] := Block[{s = {a, b}, k}, Do[k = Last@ s + 1; While[k/s[[i - 1]] <= s[[i - 1]]/s[[i - 2]], k++]; AppendTo[s, k], {i, 3, n}]; s]; S[3, 15, 10] (* Michael De Vlieger, Feb 15 2016 *)

Prog

(PARI) S(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=a[n-1]^2\a[n-2]+1); a
S(3, 15, 40) \\ Colin Barker, Feb 15 2016

Crossrefs

Sequence in context: A322186 A037759 A037647 * A019478 A151327 A037766

Adjacent sequences: A019474 A019475 A019476 * A019478 A019479 A019480

Keyword

nonn

Author

R. K. Guy

Status

approved