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A018906 Define the Shallit sequence S(a_0,a_1) by a_{n+2} is the least integer > a_{n+1}^2/a_n for n >= 0. This is S(2,6). 2
2, 6, 19, 61, 196, 630, 2026, 6516, 20957, 67403, 216786, 697242, 2242518, 7212542, 23197479, 74609345, 239963764, 771788146, 2482278709, 7983677414, 25677658524, 82586271099, 265619708576, 854304579262, 2747673800490, 8837259564290, 28423008798464 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, 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.

Jeffrey Shallit, Problem B-686, Fib. Quart., 29 (1991), 85.

FORMULA

a(n) = [ a(n-1)^2/a(n-2)+1 ].

MAPLE

a:= proc(n) option remember; `if`(n<2, [2, 6][n+1],

       1 +floor(a(n-1)^2/a(n-2)))

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, May 05 2014

MATHEMATICA

a[0]=2; a[1]=6; a[n_] := a[n] = Floor[a[n-1]^2/a[n-2]+1]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Mar 30 2015 *)

PROG

(PARI) a1n=concat([ 2, 6 ], vector(28)); a(n)=a1n[ n+1 ]; for(n=2, 29, a1n[ n+1 ]=1+floor(a(n-1)^2/a(n-2)))

CROSSREFS

There has been some confusion between A018906 and A014010. I think the descriptions are correct now, thanks to Michael Somos.

Sequence in context: A001169 A187276 A022041 * A014010 A022015 A138747

Adjacent sequences:  A018903 A018904 A018905 * A018907 A018908 A018909

KEYWORD

nonn

AUTHOR

Simon Plouffe, R. K. Guy

EXTENSIONS

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009

STATUS

approved

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Last modified August 23 11:24 EDT 2019. Contains 326222 sequences. (Running on oeis4.)