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 A000324 A nonlinear recurrence: a(n) = a(n-1)^2 - 4*a(n-1) + 4 (for n>1). (Formerly M3789 N1544) 8
 1, 5, 9, 49, 2209, 4870849, 23725150497409, 562882766124611619513723649, 316837008400094222150776738483768236006420971486980609 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An infinite coprime sequence defined by recursion. - Michael Somos, Mar 14 2004 This is the special case k=4 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 A000058, A000215, A000289 and this sequence here can be represented as values of polynomials defined via P_0(z)= 1+z, P_{n+1}(z) = z+ prod_{i=0..n} P_i(z), with recurrences P_{n+1}(z) = (P_n(z))^2 -z*P_n(z) +z, n>=0. - Vladimir Shevelev, Dec 08 2010 REFERENCES 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). LINKS T. D. Noe, 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. - 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] FORMULA a(n) = L(2^n)+2, if n>0 where L() is Lucas sequence. For n>=1, a(n) = 4+Prod{i=0,...,n-1} a(i). - Vladimir Shevelev, Dec 08 2010 MATHEMATICA t = {1, 5}; Do[AppendTo[t, t[[-1]]^2 - 4*t[[-1]] + 4], {n, 11}] (* T. D. Noe, Jun 19 2012 *) Join[{1}, RecurrenceTable[{a[n] == a[n-1]^2 - 4*a[n-1] + 4, a[1] == 5}, a, {n, 1, 8}]] (* Jean-François Alcover, Feb 07 2016 *) PROG (PARI) a(n)=if(n<2, max(0, 1+4*n), a(n-1)^2-4*a(n-1)+4) (PARI) a(n)=if(n<1, n==0, n=2^n; fibonacci(n+1)+fibonacci(n-1)+2) CROSSREFS a(n) = A001566(n-1)+2 (for n>0). Cf. A000058. Sequence in context: A328333 A173776 A289909 * A123817 A124421 A262918 Adjacent sequences:  A000321 A000322 A000323 * A000325 A000326 A000327 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 21 17:33 EDT 2021. Contains 343156 sequences. (Running on oeis4.)