[seqfan] Re: New sequence?
Neil Sloane
njasloane at gmail.com
Sat Apr 21 09:57:58 CEST 2012
Richard, I entered your sequence - it is now A182256.
Note that A000048 has a b-file giving the first 100 terms.
Neil
On Fri, Apr 20, 2012 at 5:00 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
> Well, that went over like a lead balloon! Here's what I guess to be the
> next three members of A000048: 954437120, 1857283155, 3616814565.
>
> This gives 4096, 2, 4 for the next three members of the suggested
> sequence. Conjecture: in this sequence, if n is 3-smooth. then
> a(n) is a power of 2. [probably easy to prove.]
>
> A000048 is a sort of pseudo-divisibility sequence. E.g.
>
> 2 has ranks of apparition 4, 9 and 25 (and 49, ...???) in the
> sense that A000048(n) is even just if n is a multiple of
> 4 or 9 or 25 (or 49 or ???)
>
> 5 has ranks 6, 13, 14, 17, 22, ???
>
> 7 has ranks 9, 13, 19, ??
>
> 11 has ranks 21, 25, 33, ??
>
> 13 has ranks 14, 18, 37, 38, ??
>
> 17 has ranks 10, 12, 21, 26, ??
>
> 31 has ranks 11, 25, ??
>
> However, 3 does not divide A000048(15), so maybe I'm barking
> up the wrong tree. Check? Mod 2^15 + 1, there is a 2-cycle
> {10923,-10923}, a 6-cycle {3641,7282,14564,-3641,-7282,-**14564},
> three 10-cycles of which one is
> {2979,5958,11916,-8937,14895,-**2979,-5958,...}, and 1091
> 30-cycles. R.
>
>
> On Thu, 19 Apr 2012, Richard Guy wrote:
>
> Would an editor more competent than I like to enter the following
>> sequence into OEIS, if it's not there already (I'm not a good looker) ?
>>
>> [check & extend. These are only hand calculations. A000048 could
>> also easily be extended] For n = (0) 1 2 3 ...
>>
>> (0),0,0,2,0,2,4,2,0,8,4,2,16,**2,4,38,0,2,64,2,16,134,4,2,**256,32,4,
>> 512,16,2,1084,2,0,2054,4,159,
>>
>> It's the total length of all cycles which are strictly less than
>> the full length of 2n.
>>
>> 2^n - 2 * n * A000048(n)
>>
>> a(2^k) = 0, a(prime) = 2, a(2p) = 4.
>>
>> There's a simple formula using the Moebius function (v. A000048).
>>
>> Let me know if I've made errors. Thanks! R.
>>
>>
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--
Dear Friends, I will soon be retiring from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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