cp's OEIS Frontend

A110368 Integers with mutual residues of 9.

%I A110368 #23 Jan 09 2025 09:49:10
%S A110368 10,19,199,37819,1429936399,2044718092315659619,
%T A110368 4180872077042990313463432060226288599,
%U A110368 17479691324597767931283328689425028720038746822457352536058485868000785419
%N A110368 Integers with mutual residues of 9.
%C A110368 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 A110368 A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/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.
%H A110368 A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
%H A110368 Stanislav Drastich, <a href="http://arxiv.org/abs/math/0202010">Rapid growth sequences</a>, arXiv:math/0202010 [math.GM], 2002.
%H A110368 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 A110368 S. Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer sequences with mutual k-residues</a>
%H A110368 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>.
%F A110368 a(n) ~ c^(2^n), where c = 1.9324294501525084771045650938374200605001383645783351474944965038078432359... . - _Vaclav Kotesovec_, Dec 17 2014
%t A110368 RecurrenceTable[{a[1]==10, a[n]==a[n-1]*(a[n-1]-9)+9}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 17 2014 *)
%Y A110368 Column k=9 of A177888.
%K A110368 nonn
%O A110368 1,1
%A A110368 _Seppo Mustonen_, Sep 04 2005