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

Author

R. K. Guy

Keywords

• nonn

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

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Programs

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

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

Formula

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

Extensions

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