login
A019475
Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(2,10).
1
2, 10, 51, 261, 1336, 6839, 35009, 179212, 917391, 4696149, 24039712, 123059927, 629947050, 3224715759, 16507406022, 84501851928, 432567234958, 2214323218841, 11335179646638, 58025087091309, 297031969224468, 1520514576781740, 7783554693597965
OFFSET
0,1
LINKS
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;.
MAPLE
a:= proc(n) option remember;
`if`(n<2, [2, 10][n+1], floor(a(n-1)^2/a(n-2))+1)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 18 2015
MATHEMATICA
a[n_] := a[n] = Switch[n, 0, 2, 1, 10, _, 1 + Floor[a[n-1]^2/a[n-2]]];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)
PROG
(PARI) S(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=a[n-1]^2\a[n-2]+1); a
S(2, 10, 40) \\ Colin Barker, Feb 16 2016
CROSSREFS
Sequence in context: A037514 A037717 A019476 * A020042 A353289 A307208
KEYWORD
nonn
AUTHOR
EXTENSIONS
Incorrect g.f. deleted by Alois P. Heinz, Sep 18 2015
STATUS
approved