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A022024
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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(6,66).
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2
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6, 66, 727, 8009, 88232, 972018, 10708349, 117969769, 1299627646, 14317498734, 157730385799, 1737655093709, 19143078927992, 210891949829430, 2323315631208341, 25595076182769253, 281971126093205254, 3106367622527151978, 34221659288246953735, 377006879658404795777
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OFFSET
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0,1
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COMMENTS
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This coincides with the linearly recurrent sequence defined by the expansion of (6 - 5*x^2)/(1 - 11*x - x^2 + 9*x^3) only up to n <= 169. - Bruno Berselli, Feb 11 2016
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LINKS
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FORMULA
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a(n+1) = floor(a(n)^2/a(n-1))+1 for all n > 0. - M. F. Hasler, Feb 10 2016
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MAPLE
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option remember;
if n <= 1 then
op(n+1, [6, 66]) ;
else
a := procname(n-1)^2/procname(n-2) ;
if type(a, 'integer') then
a+1 ;
else
ceil(a) ;
fi;
end if;
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MATHEMATICA
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a[n_] := a[n] = Switch[n, 0, 6, 1, 66, _, Floor[a[n-1]^2/a[n-2]]+1];
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PROG
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(PARI) a=[6, 66]; for(n=2, 30, a=concat(a, a[n]^2\a[n-1]+1)); a \\ M. F. Hasler, Feb 10 2016
(Python)
def a(n):
if n == 0: return 6
prev_1, prev_2 = 66, 6
for i in range(2, n + 1):
prev_2, prev_1 = prev_1, (prev_1 ** 2) // prev_2 + 1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Double-checked and extended to 3 lines of data by M. F. Hasler, Feb 10 2016
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STATUS
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approved
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