A022031 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(4,17).

4, 17, 72, 304, 1283, 5414, 22845, 96397, 406757, 1716352, 7242319, 30559689, 128949662, 544115986, 2295951781, 9687997993, 40879475731, 172495033261, 727860031657, 3071278144467, 12959565068034, 54684179957837, 230745362360740, 973653116715681, 4108426630946045

Offset

0,1

Comments

The empirical g.f. / recurrence agrees with the original definition for at least 2000 terms (and a(2000) ~ 10^1250). - M. F. Hasler, Feb 11 2016

Links

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

Formula

Empirical g.f.: -(x^6+x^5+x^4+x^3-x-4) / ((x-1)*(x^6+2*x^5+3*x^4+4*x^3+4*x^2+3*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) ~ 4.219599938... as n -> oo. - M. F. Hasler, Feb 11 2016

Prog

(PARI) a=[4, 17]; for(n=2, 2000, a=concat(a, ceil(a[n]^2/a[n-1])-1)); A022031(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016

Crossrefs

Cf. A022018 - A022025, A022026 - A022032.

Sequence in context: A179606 A108929 A297578 * A255117 A001076 A122451

Adjacent sequences: A022028 A022029 A022030 * A022032 A022033 A022034

Keyword

nonn

Author

R. K. Guy

Extensions

Edited by M. F. Hasler, Feb 11 2016

Status

approved