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).

6, 102, 1735, 29513, 502028, 8539699, 145263729, 2470994700, 42032617843, 714991805825, 12162299391068, 206885624804179, 3519208035780561, 59863150041598764, 1018296359995701043, 17321632357467588641, 294647962336362325244, 5012080843035687303187

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..811

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

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

Cf. A022018 - A022024, A022026 - A022032.

Sequence in context: A344400 A277662 A371250 * A302911 A174481 A306205

Adjacent sequences: A022022 A022023 A022024 * A022026 A022027 A022028

Keyword

nonn

Author

R. K. Guy

Extensions

An incorrect program was removed by Alois P. Heinz, Apr 27 2019

Status

approved