A010916 Pisot sequence E(8,10), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

8, 10, 13, 17, 22, 28, 36, 46, 59, 76, 98, 126, 162, 208, 267, 343, 441, 567, 729, 937, 1204, 1547, 1988, 2555, 3284, 4221, 5425, 6972, 8960, 11515, 14799, 19020, 24445, 31417, 40377, 51892, 66691, 85711, 110155, 141570, 181944, 233832, 300518, 386222, 496368, 637926

Offset

0,1

References

Cantor, D. G. "Investigation of T-numbers and E-sequences." In Computers in Number Theory, ed. AOL Atkin and BJ Birch, Acad. Press, NY (1971); pp. 137-140.

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

David Cantor, Investigation of T-numbers and E-sequences, In Computers in Number Theory, ed. A. O. L. Atkin and B. J. Birch, Acad. Press, NY (1971); pp. 137-140. [Annotated scanned copy]

Formula

It is not true that a(n) = a(n-1) + a(n-6), which holds just for n <= 37 (see A275627). E.g. a(38) = 110155 = 85711 + 24445 - 1 = a(37) + a(32) - 1. Sequence is believed to be non-recurring.

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, 8, 10) \\ Colin Barker, Jul 28 2016

Crossrefs

See A008776 for definitions of Pisot sequences.

Cf. A275627.

Sequence in context: A120166 A030732 A167487 * A275627 A101764 A309065

Adjacent sequences: A010913 A010914 A010915 * A010917 A010918 A010919

Keyword

nonn

Author

Simon Plouffe

Status

approved