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 A001543 a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0. (Formerly M4091 N1699) 5

%I M4091 N1699

%S 1,6,11,71,4691,21982031,483209576974811,

%T 233491495280173380882643611671,

%U 54518278368171228201482876236565907627201914279213829353891

%N a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0.

%C This is the special case k=5 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 Alois P. Heinz, <a href="/A001543/b001543.txt">Table of n, a(n) for n = 0..12</a>

%H A. V. Aho and N. J. A. Sloane, <a href="http://neilsloane.com/doc/doubly.html">Some doubly exponential sequences</a>, Fib. Quart., 11 (1973), 429-437.

%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(n) = a(n-1) * (a(n-1) - 5) + 5. - _Charles R Greathouse IV_, Dec 09 2011

%F a(n) ~ c^(2^n), where c = 1.696053774403103324180661918166106455311376345474042496749974632237971081462... . - _Vaclav Kotesovec_, Dec 17 2014

%t Flatten[{1,RecurrenceTable[{a[1]==6, a[n]==a[n-1]*(a[n-1]-5)+5}, a, {n, 1, 10}]}] (* _Vaclav Kotesovec_, Dec 17 2014 *)

%t Join[{1},NestList[#(#-5)+5&,6,10]] (* _Harvey P. Dale_, Oct 10 2016 *)

%o (PARI) {

%o print1("1, 6");

%o n=6;

%o m=Mod(5,6);

%o for(i=2,9,

%o n=m.mod+lift(m);

%o m=chinese(m,Mod(5,n));

%o print1(", "n)

%o )

%o } \\ _Charles R Greathouse IV_, Dec 09 2011

%Y Column k=5 of A177888.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E New name from _Alonso del Arte_, Dec 09 2011

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Last modified August 17 17:25 EDT 2019. Contains 326059 sequences. (Running on oeis4.)