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A000289
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A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).
(Formerly M3316 N1333)
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11
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1, 4, 7, 31, 871, 756031, 571580604871, 326704387862983487112031, 106735757048926752040856495274871386126283608871, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031
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OFFSET
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0,2
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COMMENTS
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An infinite coprime sequence defined by recursion. - Michael Somos, Mar 14 2004
This is the special case k=3 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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John Cerkan, Table of n, a(n) for n = 0..12
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.
S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012 - From N. J. A. Sloane, Jun 13 2012
S. Mustonen, On integer sequences with mutual k-residues
Seppo Mustonen, On integer sequences with mutual k-residues [Local copy]
Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
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a(n) = A005267(n) + 2 (for n>0).
a(n) = ceiling(c^(2^n)) + 1 where c = A077141. - Benoit Cloitre, Nov 29 2002
For n>0, a(n) = 3 + Product_{i=0..n-1} a(i). - Vladimir Shevelev, Dec 08 2010
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MATHEMATICA
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Join[{1}, RecurrenceTable[{a[n] == a[n-1]^2 - 3*a[n-1] + 3, a[1] == 4}, a, {n, 1, 9}]] (* Jean-François Alcover, Feb 06 2016 *)
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PROG
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(PARI) a(n)=if(n<2, max(0, 1+3*n), a(n-1)^2-3*a(n-1)+3)
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CROSSREFS
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Cf. A000058.
Sequence in context: A156228 A218959 A283332 * A241426 A271676 A149089
Adjacent sequences: A000286 A000287 A000288 * A000290 A000291 A000292
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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