A019482 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(4,28).

4, 28, 197, 1387, 9766, 68764, 484179, 3409187, 24004668, 169020968, 1190105509, 8379736191, 59003154006, 415451286688, 2925263479867, 20597279875727, 145028966176516, 1021173725712004, 7190258646781909, 50627839422302787, 356479265974341398

Offset

0,1

Comments

This coincides with the linearly recurrent sequence defined by the expansion of (4-3*x^2)/(1-7*x-x^2+5*x^3) only up to n<=55. - R. J. Mathar, Feb 10 2016

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, [4, 28][n+1], floor(a(n-1)^2/a(n-2))+1)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 10 2016

Mathematica

a[n_] := a[n] = Switch[n, 0, 4, 1, 28, _, Floor[a[n - 1]^2/a[n - 2]] + 1];
a /@ Range[0, 30] (* Jean-François Alcover, Feb 06 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(4, 28, 40) \\ Colin Barker, Feb 16 2016

Crossrefs

Sequence in context: A208704 A270471 A355354 * A198630 A246021 A090965

Adjacent sequences: A019479 A019480 A019481 * A019483 A019484 A019485

Keyword

nonn

Author

R. K. Guy

Status

approved