[seqfan] Re: A mysterious sequence found accidentally by analysis of a recycled draft.

[Thomas Scheuerle]

Thank you !

I feel embarrassed because the numbers did not tell it to me simply by looking onto them.
A interesting obfuscation.
But this list gets it all, here are some of the best puzzle solvers of the planet listening. 

Thank you Paul


On Sat, 13 Apr 2024 06:52:14 -0400
Paul Hanna <pauldhanna.math at gmail.com> wrote:

> Hi Thomas,
>       That sequence is   *(n+1)*prime(n) + 1*   for n >= 1 with a(0) = 1.
> 
> The following PARI programs have the same output for n > 0 (with
> precision):
> a(n) = round( log( abs( I*(1-I) * prod(k = 1, n, 1 - I^*prime(k)*
> )^prime(n) )^2 )/log(2) )
> a(n) = valuation( round( 2 * prod(k = 1, n, abs(1 - I^*(prime(k)%4)* )^2
> )^prime(n)  ),2)
> a(n) = valuation( 2 * 2^((n+1)*prime(n)), 2)
> 
> which is simply (n+1)*prime(n) + 1.
> - Paul
> 
> On Sat, Apr 13, 2024 at 1:37 AM Thomas Scheuerle <
> Thomas.Scheuerle at kabelbw.de> wrote:
> 
> > Dear sequence fans,
> >
> > Recently a draft from Dylan A. Elias got recycled because it was abandoned.
> > It did not contain complete information to reproduce it numbers.
> > I was curious and looked into it and its description suggested to me
> > something
> > which I did put into a PARI program here:
> >
> > a(n) = if(n=0, 1, log(abs(I*(1-I)*prod(k = 1, n,
> > 1-I^prime(k))^prime(n))^2)/log(2))
> >
> > It gives the sequence:
> >
> > 1,5,10,21,36,67,92,137,172,231,320,373,482,575,646,753,902,1063,1160,1341,1492,1607,1818,1993,2226,2523,2728,2885,3104,3271,3504,4065,...
> >
> > This is not the same sequence the author did originally propose as I
> > failed to reproduce or understand the idea properly.
> >
> > This sequence is for me mysterious and puzzling, could it be interesting?
> > It has odd and even terms interleaved.
> > A084310(n) = gcd(n,a(n)) appears to hold by observation.
> > Does anyone know into which topic this sequence may belong?
> >
> > thank you very much
> >
> > Thomas
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> 
> --
> Seqfan Mailing list - http://list.seqfan.eu/


-- 
Thomas Scheuerle <Thomas.Scheuerle at kabelbw.de>