Near Integers

[Artur]

Dear Max and Seqfans,
Of course I'm agree that recent title is better. Also sign < have to be  
changed on <=.
But I was interpreted previous title exactly follow Ribenboim book and  
word divided was treated as divided modulo p (not exactly that a!/p^m is  
integer)
If we take a=6 and p=5 sample from the book formula will be following
a! = 720 = 1*5^4 + 0*5^3 + 3*5^2 + 4*5^1 + 0
and 5^4<=720<5^5 and from these reason 4 is a(6) in A127032
In pentanary positional system 6! is number 10340

BEST WISHES
ARTUR


Dnia 05-01-2007 o 09:40:45 Max A. <maxale at gmail.com> napisał(a):

> Artur and SeqFans,
>
> I've checked the book "The Little Book of Big Primes" (2nd ed.) by
> Ribenboim, Section 2.D at page 24. It indeed states the following:
>
> "In 1808, Legendre the exact power p^m of the prime p that divides a
> factorial a! (so that p^(m+1) does not divide a!)."
>
> which seems to be consistent with the comment
>
> %C A125552 A. M. Legendre in 1808 gave a formula for finding m.
>
> and similar comments in other sequences (A127032, A127033, A127034,
> A127035, A127036, A127037, A127039). There is a problem, though.
>
> The Legendre's formula is irrelevant to these sequences, since it
> indeed determines the maximum power of p *dividing* n! (as Ribenboim
> said) while Artur's sequences define the maximum power of p *not
> exceeding* n!.
> So the comments like the one quoted above should be removed from these
> sequences.
>
> P.S. As I see, Neil has already corrected these sequences according to
> my previous message. That's fine but somehow "less or equal" symbol in
> the sequence names got incorrectly replaced with strict < symbol.
> Neil, please fix it up as well.
>
> Thanks,
> Max
>
> On 1/4/07, Artur <grafix at csl.pl> wrote:
>> Dear Max,
>> I was take these title from Ribenboim book 2.2.4
>> ARTUR
>>
>> Dnia 04-01-2007 o 22:08:11 Max A. <maxale at gmail.com> napisał(a):
>>
>> > On 1/4/07, N. J. A. Sloane <njas at research.att.com> wrote:
>> >
>> >> Also, just to make things more difficult, Artur submitted several  
>> pairs
>> >> of sequences with the same A-numbers, for example:
>> >> %I A127030
>> >> %S A127030 0, 1, 2, 4, 5, 7, 9, 11, 13, 15, 18, 20, 22
>> >> %N A127030 Maximal value of power m such that 3^m divided n! (3^m  
>> <
>> >> n!)
>> >
>> > I think the name of this and other similar sequences (A127032,
>> > A127033, A127034, A127035, A127036, A127037, A127039) is confusing. It
>> > has nothing to do with the division (but rather with taking a
>> > logarithm), and it should be renamed to
>> > "Maximal value of power m such that 3^m < n!"
>> > with a formula
>> > a(n) = floor( log(n!) / log(3) ).
>> >
>> > Max
>>
>>
>>