[seqfan] Re: A100071 - query re comment and reference

[Vladimir Shevelev]

Using Zumkeller's formula a(n)=n/floor(n/2)*a(n-1), n>=1, it is easy to prove the following beautiful property of A100071: beginning with the least term multiple of an odd prime p (which is a(p)), we have p+1 consecutive terms multiple of p, i.e., up to a(2*p), such that a(2*p+1) is not multiple of p.
 
Regards,
Vladimir

----- Original Message -----
From: Peter Luschny <peter.luschny at gmail.com>
Date: Friday, August 17, 2012 10:29
Subject: [seqfan] Re: A100071 - query re comment and reference
To: seqfan at list.seqfan.eu

> DS > A comment on this sequence says:
> DS > "Corollary 3 of "An Identity Involving the Least Common 
> Multiple of
> DS > Binomial Coefficients and its Application" mentions this 
> sequence"DS > Is this true?
> 
> The expression in the third line of the proof of Corollary 3 gives:
> 
> seq(max(seq(n*binomial(n-1,i),i=0..n-1)),n=1..6);
> 1, 2, 6, 12, 30, 60,...
> 
> Roger L. Bagula used this in his implementation of A100071
> Table[If[n == 0, 0, n*Binomial[n - 1, Floor[(n - 1)/2]]], {n, 0, 30}]
> 
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 Shevelev Vladimir‎