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A181908 Least k such that log(ceiling(sqrt(k!))^2-k!)/k > n. 0
17, 145, 1095, 8098, 59868, 442406, 3269011 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence show how quickly A068869 increase in a logarithmic scale.
LINKS
EXAMPLE
a(1)=17 because log(ceiling(sqrt(17!))^2-17!)/17 = 1.00471 > 1.
MATHEMATICA
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}]
PROG
(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
CROSSREFS
Cf. A068869.
Sequence in context: A216422 A008417 A241796 * A233328 A364155 A083294
KEYWORD
nonn,hard,more
AUTHOR
Artur Jasinski, Apr 01 2012
EXTENSIONS
a(6)-a(7) from Charles R Greathouse IV, Apr 03 2012
STATUS
approved

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Last modified April 17 07:13 EDT 2024. Contains 371756 sequences. (Running on oeis4.)