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

0,1

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Sequence in context: A067403 A173292 A173558 * A058410 A005979 A165225

Adjacent sequences: A022019 A022020 A022021 * A022023 A022024 A022025

Keyword

nonn

Author

R. K. Guy

Extensions

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

Status

approved