%I #20 Apr 07 2021 02:49:57
%S 10,19,199,37819,1429936399,2044718092315659619,
%T 4180872077042990313463432060226288599,
%U 17479691324597767931283328689425028720038746822457352536058485868000785419
%N Integers with mutual residues of 9.
%C This is the special case k=9 of sequences with exact mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))=k, i=1,...,n-1}. k=1 gives Sylvester's sequence A000058 and k=2 Fermat sequence A000215.
%H A. V. Aho and N. J. A. Sloane, <a href="https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, <a href="http://neilsloane.com/doc/doubly.html">alternative link</a>.
%H Stanislav Drastich, <a href="http://arxiv.org/abs/math/0202010">Rapid growth sequences</a>, arXiv:math/0202010 [math.GM], 2002.
%H S. W. Golomb, <a href="http://www.jstor.org/stable/2311857">On certain nonlinear recurring sequences</a>, Amer. Math. Monthly 70 (1963), 403-405.
%H S. Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer sequences with mutual k-residues</a>
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>.
%F a(n) ~ c^(2^n), where c = 1.9324294501525084771045650938374200605001383645783351474944965038078432359... . - _Vaclav Kotesovec_, Dec 17 2014
%t RecurrenceTable[{a[1]==10, a[n]==a[n-1]*(a[n-1]-9)+9}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 17 2014 *)
%Y Column k=9 of A177888.
%K nonn
%O 1,1
%A _Seppo Mustonen_, Sep 04 2005