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A001544 A nonlinear recurrence.
(Formerly M4346 N1820)
5

%I M4346 N1820

%S 1,7,13,97,8833,77968897,6079148431583233,

%T 36956045653220845240164417232897,

%U 1365749310322943329964576677590044473746108255675592519835615233

%N A nonlinear recurrence.

%C This is the special case k=6 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. - _Seppo Mustonen_, Sep 04 2005

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Indranil Ghosh, <a href="/A001544/b001544.txt">Table of n, a(n) for n = 0..11</a>

%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 R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012. - _N. J. A. Sloane_, Jun 13 2012

%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(0)=1, a(1)=7, a(n)=a(n-1)^2-6*a(n-1)+6 if n>1.

%F a(n) ~ c^(2^n), where c = 1.76450357631319101484804524709844019487003729926754942591419313922841785792... . - _Vaclav Kotesovec_, Dec 17 2014

%t Flatten[{1,RecurrenceTable[{a[1]==7, a[n]==a[n-1]*(a[n-1]-6)+6}, a, {n, 1, 10}]}] (* _Vaclav Kotesovec_, Dec 17 2014 *)

%o (PARI) a(n)=if(n<1, n==0, if(n==1, 7, n=a(n-1); n^2-6*n+6))

%Y Column k=6 of A177888. - _Alois P. Heinz_, Nov 07 2012

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)