A010902 Pisot sequence E(14,23), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).

14, 23, 38, 63, 104, 172, 284, 469, 775, 1281, 2117, 3499, 5783, 9558, 15797, 26109, 43152, 71320, 117875, 194819, 321989, 532170, 879548, 1453680, 2402581, 3970885, 6562912, 10846905, 17927308, 29629500, 48970390, 80936199, 133767942, 221086022, 365401668

Offset

0,1

Links

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

D. W. Boyd, Pisot sequences which satisfy no linear recurrences, Acta Arith. 32 (1) (1977) 89-98

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, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

Formula

It is known (Boyd, 1977) that this sequence does not satisfy a linear recurrence. - N. J. A. Sloane, Aug 07 2016

Mathematica

RecurrenceTable[{a[1] == 14, a[2] == 23, a[n] == Floor[a[n-1]^2/a[n-2]+1/2]}, a, {n, 40}] (* Vincenzo Librandi, Aug 09 2016 *)

Prog

(PARI) pisotE(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]+1/2));
  a
}
pisotE(50, 14, 23) \\ Colin Barker, Jul 28 2016
(Python)
a, b = 14, 23
A010902_list = [a, b]
for i in range(1000):
    c, d = divmod(b**2, a)
    a, b = b, c + (0 if 2*d < a else 1)
    A010902_list.append(b) # Chai Wah Wu, Aug 08 2016

Crossrefs

Cf. A008776.

Sequence in context: A026065 A316735 A010922 * A010923 A015850 A020905

Adjacent sequences: A010899 A010900 A010901 * A010903 A010904 A010905

Keyword

nonn

Author

Simon Plouffe

Status

approved