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A001544
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A nonlinear recurrence.
(Formerly M4346 N1820)
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5
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(0)=1, a(1)=7, a(n)=a(n-1)^2-6*a(n-1)+6 if n>1.
a(n) ~ c^(2^n), where c = 1.76450357631319101484804524709844019487003729926754942591419313922841785792... . - Vaclav Kotesovec, Dec 17 2014
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=if(n<1, n==0, if(n==1, 7, n=a(n-1); n^2-6*n+6))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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