A010918 Shallit sequence S(8,55): a(n) = floor(a(n-1)^2/a(n-2) + 1).

8, 55, 379, 2612, 18002, 124071, 855106, 5893451, 40618081, 279942687, 1929384798, 13297456486, 91647010581, 631637678776, 4353291555505, 30003193292641, 206784130187015, 1425170850320396, 9822378297435246, 67696525926163327, 466569244606302614

Offset

0,1

Comments

Agrees with A019484 for terms 0 through 11055 but then differs from it. It is not known if S(8,55) satisfies a linear recurrence.

a(11056) = 4971494197...7586894095 (9270 digits) = A019484(11056) + 1. - Jianing Song, Oct 15 2021

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.

Index entries for sequences which agree for a long time but are different

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 A308687 * A019484 A108984 A264342

Adjacent sequences: A010915 A010916 A010917 * A010919 A010920 A010921

Keyword

nonn

Author

N. J. A. Sloane and Simon Plouffe

Status

approved