A181908 Least k such that log(ceiling(sqrt(k!))^2-k!)/k > n.

17, 145, 1095, 8098, 59868, 442406, 3269011

Offset: 1

Author

Artur Jasinski, Apr 01 2012

Keywords

• nonn
• hard
• more

Comments

This sequence show how quickly A068869 increase in a logarithmic scale.

Examples

			a(1)=17 because log(ceiling(sqrt(17!))^2-17!)/17 = 1.00471 > 1.
		

Crossrefs

Cf. A068869.

Programs

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}]

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

Extensions

a(6)-a(7) from Charles R Greathouse IV, Apr 03 2012