A022027 Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(2,16).

2, 16, 127, 1008, 8000, 63492, 503904, 3999232, 31739888, 251903488, 1999230976, 15866888256, 125927492096, 999423012864, 7931916549888, 62951622430720, 499615287394304, 3965194632954880, 31469750573916160, 249759543441752064, 1982215569002196992, 15731845549721911296

Offset

0,1

Comments

Not to be confused with the Pisot T(2,16) sequence, which is A013730. - R. J. Mathar, Feb 13 2016

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

Formula

Conjectures: a(n) = 8*a(n-1)-4*a(n-3). G.f.: -(x^2-2) / (4*x^3-8*x+1). - Colin Barker, Sep 18 2015

a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - M. F. Hasler, Feb 11 2016

Mathematica

RecurrenceTable[{a[1] == 2, a[2] == 16, a[n] == Ceiling[a[n-1]^2 / a[n-2] - 1]}, a, {n, 30}] (* Vincenzo Librandi, Feb 12 2016 *)

Prog

(PARI) a=[2, 16]; for(n=2, 1000, a=concat(a, ceil(a[n]^2/a[n-1])-1)); A022027(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016
(Magma) I:=[2, 16]; [n le 2 select I[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..30]]; // Vincenzo Librandi, Feb 12 2016

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Sequence in context: A069868 A338186 A208073 * A322297 A338933 A013730

Adjacent sequences: A022024 A022025 A022026 * A022028 A022029 A022030

Keyword

nonn

Author

R. K. Guy

Extensions

Double-checked (original definition agrees with g.f. / recurrence for n=0..1000), extended and edited by M. F. Hasler, Feb 11 2016

Status

approved