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A181908
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Least k such that log(ceiling(sqrt(k!))^2-k!)/k > n.
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0
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OFFSET
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1,1
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COMMENTS
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This sequence show how quickly A068869 increase in a logarithmic scale.
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LINKS
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EXAMPLE
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a(1)=17 because log(ceiling(sqrt(17!))^2-17!)/17 = 1.00471 > 1.
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MATHEMATICA
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kkk = 0; n = 1; Do[While[kkk < max, n++; kk = Floor[Sqrt[n!]]; kkk = N[Log[(kk + 1)^2 - n!]/n]]; Print[n], {max, 1, 5}]
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PROG
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(PARI) a(n)=my(k=solve(x=1, 4<<(3*n), (log(2)+lngamma(x+1)/2)/x-n)\1, f=k!); while(n>log((sqrtint(f*=k++)+1)^2-f)/k, ); k \\ Charles R Greathouse IV, Apr 03 2012
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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