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A010918 Shallit sequence S(8,55): a(n) = [a(n-1)^2/a(n-2)+1]. 2
8, 55, 379, 2612, 18002, 124071, 855106, 5893451, 40618081, 279942687, 1929384798, 13297456486, 91647010581, 631637678776, 4353291555505, 30003193292641, 206784130187015, 1425170850320396, 9822378297435246, 67696525926163327, 466569244606302614 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Agrees with A019484 for terms 0 through 11056 but then differs from it. It is not known if S(8,55) satisfies a linear recurrence.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.

Jeffrey Shallit, Problem B-686, Fib. Quart., 29 (1991), 85.

PROG

(PARI) pisotS(nmax, a1, a2) = {

  a=vector(nmax); a[1]=a1; a[2]=a2;

  for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1));

  a

}

pisotS(50, 8, 55) \\ Colin Barker, Aug 09 2016

CROSSREFS

Sequence in context: A033890 A010924 * A019484 A108984 A264342 A230963

Adjacent sequences:  A010915 A010916 A010917 * A010919 A010920 A010921

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Simon Plouffe

STATUS

approved

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Last modified October 19 06:19 EDT 2018. Contains 316336 sequences. (Running on oeis4.)