Intended for: July 5, 2012
Timetable
- First draft entered by Alonso del Arte on March 6, 2011 based on an almost verbatim copy of a write-up by Charles Greathouse from October 20, 2010. ✓
- Draft reviewed by Alonso del Arte on April 30, 2011 ✓
- Draft approved by T. D. Noe June 5, 2011 ✓
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A177854: Smallest prime of rank
.
-
{ 2, 3, 11, 131, 1571, 43717, 5032843, 1047774137, ... }
This is a re-imagination of the
Erdős–Selfridge classification of primes.
2 is rank
0 by definition, and for other
primes the rank is the lesser of the maximum rank of the primes dividing
and the maximum rank of the primes dividing
.
There are many interesting questions that could be asked about this sequence. What are
,
, and
? The sequence is infinite: how closely can its growth be bounded? (Look at the
logarithmic graph, it seems to follow quite close to a regular pattern.) How does the closely-related sequence
A169818 behave around random large integers? (This last question is related to the performance of modern
algorithms!)
Trivial bounds: If
and
are the smallest primes of rank
, then the smallest prime of rank
is at least
and at most
where
is
Linnik’s constant. These give rise to bounds like
and
, respectively.