A019475 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(2,10).

2, 10, 51, 261, 1336, 6839, 35009, 179212, 917391, 4696149, 24039712, 123059927, 629947050, 3224715759, 16507406022, 84501851928, 432567234958, 2214323218841, 11335179646638, 58025087091309, 297031969224468, 1520514576781740, 7783554693597965

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, [2, 10][n+1], floor(a(n-1)^2/a(n-2))+1)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 18 2015

Mathematica

a[n_] := a[n] = Switch[n, 0, 2, 1, 10, _, 1 + Floor[a[n-1]^2/a[n-2]]];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

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(2, 10, 40) \\ Colin Barker, Feb 16 2016

Crossrefs

Sequence in context: A037514 A037717 A019476 * A020042 A353289 A307208

Adjacent sequences: A019472 A019473 A019474 * A019476 A019477 A019478

Keyword

nonn

Author

R. K. Guy

Extensions

Incorrect g.f. deleted by Alois P. Heinz, Sep 18 2015

Status

approved