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Template:Sequence of the Day for February 20

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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

The line below marks the end of the <noinclude> ... </noinclude> section.



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 np < q < (2 n + 1) p
? As
2 n
gets larger, the available primes get larger and correspondingly so does
(2 n + 1) p  −  2 np = 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.