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A022025
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(6,102).
11
6, 102, 1735, 29513, 502028, 8539699, 145263729, 2470994700, 42032617843, 714991805825, 12162299391068, 206885624804179, 3519208035780561, 59863150041598764, 1018296359995701043, 17321632357467588641, 294647962336362325244, 5012080843035687303187
OFFSET
0,1
LINKS
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.
FORMULA
The conjectured g.f. (6-5*x^2)/(1-17*x-x^2+14*x^3) yields the same initial terms a(0..271) but from a(272) on a different sequence. - Bruno Berselli and M. F. Hasler, Feb 11 2016
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, [6, 102][n+1], floor(a(n-1)^2/a(n-2))+1)
end:
seq(a(n), n=0..20); # Alois P. Heinz, Sep 18 2015
MATHEMATICA
a[n_] := a[n] = Switch[n, 0, 6, 1, 102, _, 1 + Floor[a[n-1]^2/a[n-2]]];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)
PROG
(PARI) a=[6, 102]; 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
An incorrect program was removed by Alois P. Heinz, Apr 27 2019
STATUS
approved