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).

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

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