a puzzling sequence

David Wilson davidwwilson at comcast.net
Sat May 26 17:38:29 CEST 2007

I'm guessing a panicky high-school student entered several homework problems 
into a single sequence using his mom's e-mail address.

My guess as to the original problems:

98,72,77,49,54,20 (Alternately multiply digits and add 5).

10,1,11,2,13,4,17,8,25,7 (Alternately add digits and add last two terms).

1,2,2,6,3,12,4,20,5 (Interleave positive integers and pronics).

15,20,13,18,11 (Alternately add 5 and subtract 7).

0,0,4,9,8,18,12,27 (Interleave nonnegative multiples of 4 and 9).

----- Original Message ----- 
From: "N. J. A. Sloane" <njas at research.att.com>
To: <seqfan at ext.jussieu.fr>
Sent: Saturday, May 26, 2007 7:46 AM
Subject: a puzzling sequence

> Dear Seqfans,  can anyone explain this sequence?
> Neil
> %I A120310
> %S A120310 
> 98,72,77,49,54,20,10,1,11,2,13,4,17,8,25,7,1,2,2,6,3,12,4,20,5,15,20,
> %T A120310 13,18,11,0,0,4,9,8,18,12,27
> %N A120310 Homework!
> %C A120310 Need to find the next 3 terms.
> %Y A120310 Adjacent sequences: A120307 A120308 A120309 this_sequence 
> A120311 A120312 A120313
> %Y A120310 Sequence in context: A122128 A114430 A033418 this_sequence 
> A106136 A095605 A095589
> %K A120310 nonn,unkn
> %O A120310 0,1
> %A A120310 Sydney Richardson (AmyNStiers(AT)aol.com), Aug 16 2006
> -- 
> No virus found in this incoming message.
> Checked by AVG Free Edition.
> Version: 7.5.472 / Virus Database: 269.8.0/819 - Release Date: 5/26/2007 
> 10:47 AM

I just submitted the following sequence.

>%S A000001 1,1,2,4,8,16,48,128,432,1024,4320
>%N A000001 a(n) = Number of positive integers which are coprime to n!! and 
>are <= n!! (where n!! = n*(n-2)*(n-4)*..*(1 or 2)).
>%F A000001 a(n) = a(n-2)*(n-1) if n is prime. a(n) = a(n-2)*(n-2) if n is 
>even and n/2 = an odd prime. a(n) = a(n-2)*n otherwise.
>%Y A000001 A006882,A048855
>%O A000001 1
>%K A000001 ,more,nonn,

I am pretty absolutely sure that I am right about the recursion in the 
F-line. But I am not absolutely absolutely sure I am correct.

Did I make a mistake? (Sorry for the dumb question. But I thought I 
better double-check with seq.fan, since EIS entries are suppose to be 
totally accurate.)

Leroy Quet

Divid,  that's exactly what I concluded after seeing
the earlier comments on this sequence, and it's
already been updated accordingly (and the more
interesting rows have been
added as new entries)


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