The On-Line Encyclopedia of Integer Sequences (OEIS)

A010916 revision #13

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

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OFFSET

0,1

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.

FORMULA

It is not true that a(n) = a(n-1) + a(n-6) - 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));

}

pisotE(50, 8, 10) \\ Colin Barker, Jul 28 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A120166 A030732 A167487 * A275627 A101764 A309065

Adjacent sequences: A010913 A010914 A010915 * A010917 A010918 A010919