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A022021 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(5,20). 1
5, 20, 81, 329, 1337, 5434, 22086, 89767, 364852, 1482917, 6027219, 24497237, 99567416, 404685244, 1644816681, 6685249720, 27171759829, 110437838993, 448867366641, 1824392026070, 7415121953942, 30138277741915, 122495056843392, 497873139253657, 2023572780632275 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This coincides with the linearly recurrent sequence defined by the expansion of (5 - 4*x^2)/(1 - 4*x - x^2 + 3*x^3) only up to n <= 39. - Bruno Berselli, Feb 11 2016

LINKS

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

FORMULA

a(n+1) = floor(a(n)^2/a(n-1))+1 for all n > 0. - M. F. Hasler, Feb 10 2016

MAPLE

A022021 := proc(n)

    option remember;

    if n <= 1 then

        op(n+1, [5, 20]) ;

    else

        a := procname(n-1)^2/procname(n-2) ;

        if type(a, 'integer') then

            a+1 ;

        else

            ceil(a) ;

        fi;

    end if;

end proc: # R. J. Mathar, Feb 10 2016

PROG

(PARI) a=[5, 20]; for(n=2, 30, a=concat(a, a[n]^2\a[n-1]+1)); a \\ M. F. Hasler, Feb 10 2016

CROSSREFS

Cf. A022018 - A022025, A022026 - A022032.

Sequence in context: A271196 A033131 A321703 * A165203 A249946 A030520

Adjacent sequences:  A022018 A022019 A022020 * A022022 A022023 A022024

KEYWORD

nonn

AUTHOR

R. K. Guy

EXTENSIONS

Double-checked and extended to 3 lines of data by M. F. Hasler, Feb 10 2016

STATUS

approved

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Last modified August 18 07:30 EDT 2019. Contains 326072 sequences. (Running on oeis4.)