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A019480 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(4,12) (agrees with A019481 for n <= 19 only). 3
4, 12, 37, 115, 358, 1115, 3473, 10818, 33697, 104963, 326950, 1018419, 3172281, 9881362, 30779529, 95875387, 298642966, 930245227, 2897627873, 9025842914, 28114666162, 87574585658, 272786737320, 849705465331, 2646753962113, 8244393877392, 25680524664755 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2025

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, [4, 12][n+1], floor(a(n-1)^2/a(n-2))+1)

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Sep 18 2015

MATHEMATICA

S[a_, b_, n_] := Block[{s = {a, b}, k}, Do[k = Last@ s + 1; While[k/s[[i - 1]] <= s[[i - 1]]/s[[i - 2]], k++]; AppendTo[s, k], {i, 3, n}]; s]; S[4, 12, 14] (* Michael De Vlieger, Feb 15 2016 *)

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(4, 12, 40) \\ Colin Barker, Feb 15 2016

CROSSREFS

Sequence in context: A196918 A099098 A019481 * A192907 A280891 A149319

Adjacent sequences:  A019477 A019478 A019479 * A019481 A019482 A019483

KEYWORD

nonn

AUTHOR

R. K. Guy

STATUS

approved

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Last modified June 2 07:15 EDT 2020. Contains 334767 sequences. (Running on oeis4.)