[seqfan] Re: Length of binary representation of n^3
M. F. Hasler
oeis at hasler.fr
Tue Oct 27 20:22:18 CET 2020
On Tue, 27 Oct 2020, 14:16 JEREMY GARDINER via wrote:
> A070939 Length of binary representation of n.
> A004221 10*log_10 (n) rounded up.
> Calculating A070939(n^3) I noticed some similarity to the terms of
This is because
log_2 ( n^3 ) = 3 log_10 ( n ) / log_10 ( 2 ) = 9.966 log_10 ( n )
because as we know well,
log_10 ( 2 ) = 0.30103
is very close 3/10.
So when this and 10 log_10 ( n ) are rounded up, it gives often the same as
long as the result is not larger than ~ 10^2, but not beyond that.
For the values of n where A070939(n^3) differs from A004221(n) I find:
> I'm happy to submit this sequence if anyone thinks it is interesting
> Jeremy Gardiner
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