[seqfan] Re: Producing primes from powers of 2

[Allan Wechsler]

Assuming David Corneth meant "(least power *of 2* greater than ...", then I
think this is not right because Ali Sada insists that once you begin using
a new power of 2, you can't go back to a smaller one. The first divergence
with David's guess is at a(6), which if we were using the *smallest* possible
power of 2, would be 8 + a(5) - p(5) = 8 + 6 - 13 = 1.

On Thu, Jan 28, 2021 at 8:01 AM David Corneth <davidacorneth at gmail.com>
wrote:

> Is this a(0) = 0, a(n) = (Least power greater than or equal to (prime(n) -
> a(n-1))) - prime(n) + a(n-1)?
>
> On Wed, Jan 27, 2021 at 10:20 AM Ali Sada via SeqFan <
> seqfan at list.seqfan.eu>
> wrote:
>
> > Hi Everyone,
> >
> > We want to produce prime numbers out of “blocks” of powers of 2. Each
> time
> > we use one block in addition to the remains of the previous block. When
> we
> > start using a block of size 2^k, we cannot go back later and use smaller
> > blocks.
> >
> > To get 2, we need a block of 2. So, a(1) = 2-2 = 0
> >
> > a(1) = 0
> >
> > To get 3, we need a block of 4. So, a(2) = 4-3 = 1
> >
> > a(2) = 1
> >
> > To get 5, we need a block of 4 in addition to the remains of the previous
> > block. a(3) = 4+1-5 = 0.
> >
> > a(3) = 0
> >
> > We continue:
> >
> > a(4) = 8-7 = 1
> >
> > a(5) = 16+1-11= 6
> >
> > a(6) = 16+6-13 = 9
> >
> > a(7) = 16+9-17= 8
> >
> > a(8) = 16+8-19 = 5
> >
> > a(9) = 32+5-23 = 14
> >
> > and so on.
> >
> > This is the sequence we get:
> >
> > 0, 1, 0, 1, 6, 9, 8, 5, 14, 17, 18, 13, 4, 25, 42, 53, 58, 61, 58, 51,
> 42,
> > 27, 8, 47, 78, 105, 130, 151, 170, 185, 186, 183, 174, 163, 142, 119, 90,
> > 55, 16, 99, 176, 251, 316, 379, 438, 495, 540, 573, 602, 629, 652, 669,
> > 684, 689, 688, 681, 668, 653, 632, 607, 580, 543, 492, 437, 380, 319,
> 244,
> > 163, 72
> >
> >
> >
> > I calculated 10,000 terms, and the graph seems like a “smooth”
> > quasiperiodic function.
> >
> >
> > I would really appreciate your help defining this sequence.
> >
> >
> > Best,
> >
> >
> > Ali
> >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
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>