[seqfan] Re: Producing primes from powers of 2

[David Corneth]

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
>
>
>
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>