A110360 - OEIS

%I #23 Jan 09 2025 09:48:30

%S 9,17,161,24641,606981761,368426853330807041,

%T 135738346255240000293762417728719361,

%U 18424898644107427010977107148874723523180059431182608785043639266493441

%N Integers with mutual residues of 8.

%C This is the special case k=8 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://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 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 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 = 1.8813701045812484604409881785833034768479650739052732570542874567824022000... . - _Vaclav Kotesovec_, Dec 17 2014

%t RecurrenceTable[{a[1]==9, a[n]==a[n-1]*(a[n-1]-8)+8}, a, {n, 1, 10}] (* _Vaclav Kotesovec_, Dec 17 2014 *)

%Y Column k=8 of A177888.

%K nonn

%O 1,1

%A _Seppo Mustonen_, Sep 04 2005