A022028 - OEIS

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

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OFFSET

0,1

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

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

PROG

(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

CROSSREFS

Cf. A022018 - A022025, A022026 - A022032.

Sequence in context: A115418 A163952 A246213 * A013776 A174491 A022019

Adjacent sequences: A022025 A022026 A022027 * A022029 A022030 A022031

KEYWORD

nonn

AUTHOR

R. K. Guy

STATUS

approved