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A064780
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Number of times n occurs in A000195.
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3
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2, 5, 13, 34, 94, 255, 693, 1884, 5123, 13923, 37848, 102880, 279659, 760191, 2066413, 5617093, 15268842, 41505017, 112822331, 306682895, 833650539, 2266097112, 6159890600, 16744318683, 45515777208, 123724710091
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OFFSET
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0,1
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COMMENTS
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Lim_{n->infinity} a(n+1)/a(n) = e. - Franz Vrabec, Nov 29 2014
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LINKS
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FORMULA
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a(n) = floor(exp(n+1))-floor(exp(n)), n>0.
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MAPLE
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floorexp:= proc(n) local j, s, t;
s:= 0;
t:= 1;
for j from 0 do
s:= s+t;
if j > n and t*n/(j+1-n) < 1 - frac(s) then
return floor(s)
fi;
t:= t*n/(j+1);
od
end proc:
B:= [0, seq(floorexp(i), i=1..101)]:
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MATHEMATICA
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lista = Table[Floor[Log[n]], {n, 10000000}]; Table[Length@Cases[lista, i], {i, 0, 15}] (* José María Grau Ribas, May 16 2013 *)
f[n_] := Floor[ Exp[n + 1]] - Floor[ Exp[ n]]; f[0] = 2; Array[f, 26, 0] (* Robert G. Wilson v, Mar 15 2015 *)
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PROG
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(PARI) { default(realprecision, 100); for (n=0, 200, if (n, a=floor(exp(n + 1)) - floor(exp(n)), a=2); write("b064780.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 25 2009
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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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STATUS
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approved
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