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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).
1
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Double-checked and edited by M. F. Hasler, Feb 10 2016
STATUS
approved