A022022 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(5,45).

5, 45, 406, 3664, 33067, 298425, 2693244, 24306152, 219359637, 1979690177, 17866428166, 161242026212, 1455186832835, 13132858524565, 118522219370436, 1069646525028644, 9653410934956277, 87120689404042085, 786252089896134534, 7095815621924558952, 64038747861388870507

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Comments

This coincides with the linearly recurrent sequence defined by the expansion of (5 - 4*x^2)/(1 - 9*x - x^2 + 7*x^3) only up to n <= 103. - Bruno Berselli, Feb 11 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Programs

Maple

a:= proc(n) option remember;
      `if`(n<2, [5, 45][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

nxt[{a_,b_}]:=Module[{c=Ceiling[b^2/a]},c=If[c<=b^2/a,c+1,c];{b,c}]; Transpose[NestList[nxt,{5,45},20]][[1]] (* Harvey P. Dale, Feb 11 2014 *)

PARI

a=[5,45];for(n=2,30,a=concat(a,a[n]^2\a[n-1]+1));a \\ M. F. Hasler, Feb 10 2016

Formula

a(n+1) = floor(a(n)^2/a(n-1))+1 for all n > 0. - M. F. Hasler, Feb 10 2016

Extensions

Double-checked and edited by M. F. Hasler, Feb 10 2016