A022023 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(6,30).

6, 30, 151, 761, 3836, 19337, 97477, 491378, 2477019, 12486565, 62944332, 317300149, 1599498817, 8063016906, 40645382751, 204891935393, 1032852992092, 5206575364849, 26246162074765, 132305973770306, 666949729466899, 3362069972805741, 16948075698414380

Offset

0,1

Comments

This coincides with the linearly recurrent sequence defined by the expansion of (6 - 5*x^2)/(1 - 5*x - x^2 + 4*x^3) only up to n <= 69. - 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

A022023 := proc(n)
    option remember;
    if n <= 1 then
        op(n+1, [6, 30]) ;
    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=[6, 30]; 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: A252699 A054117 A033132 * A066534 A126474 A127017

Adjacent sequences: A022020 A022021 A022022 * A022024 A022025 A022026

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