Template:Sequence of the Day for February 20

Intended for: February 20, 2013

Timetable

• First draft entered by Alonso del Arte on February 1, 2012 ✓
• Draft reviewed by Daniel Forgues on February 19, 2016 ✓
• Draft to be approved by January 20, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A205601: Goldbach’s problem extended to division: number of decompositions of

2 n

into the floor of unordered ratios of two primes,

⌊  q / p⌋ = 2 n

, where

p < 2 n < q, n   ≥   1

.

{ 0, 1, 3, 5, 4, 5, 10, 5, 10, ... }

Essentially, what we are counting here is this: for each prime

p < 2 n

, how many primes are there in the range

2 n p < q < (2 n + 1) p

? As

2 n

gets larger, the available primes get larger and correspondingly so does

(2 n + 1) p  −  2 n p = p

. Consider for example, 8, which can’t be represented as

⌊  q / 3⌋

with the constraints specified here, but both

⌊  41 / 5⌋

and

⌊  43 / 5⌋

give the desired result.