A022028 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(2,32).

2, 32, 511, 8160, 130304, 2080776, 33227136, 530591744, 8472821696, 135299330048, 2160544546816, 34500930175488, 550932488167424, 8797635454304256, 140486159827464192, 2243371097334087680, 35823556473710968832, 572053014300755787776, 9134901260033419902976

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Comments

Not to be confused with the Pisot T(2,32) sequence as defined in A008776, which is A013776. - R. J. Mathar, Feb 13 2016

Links

• Colin Barker, Table of n, a(n) for n = 0..830
• Index entries for Pisot sequences

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Programs

PARI

a=[2,32];for(n=2,2000,a=concat(a,ceil(a[n]^2/a[n-1])-1));A022028(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016

Formula

Conjecture: a(n) = 16*a(n-1)-8*a(n-3). G.f.: -(x^2-2) / (8*x^3-16*x+1). - Colin Barker, Sep 18 2015

a(n+1) = ceiling(a(n)^2/a(n-1))-1 for all n > 0. a(n+1)/a(n) ~ 15.968627... as n -> oo. - M. F. Hasler, Feb 11 2016