Intended for: October 25, 2012
Timetable
- First draft entered by Alonso del Arte based on comments by Robert G. Wilson v on October 23, 2011 ✓
- Draft to be reviewed by August 25, 2012
- Draft to be approved by September 25, 2012
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A006508:
-th composite number [actually, nonprime (i.e. unit or composite) positive integer], with
.
-
{ 1, 4, 9, 16, 26, 39, 56, 78, ... }
This sequence is generated by a
sieve: start with the
natural numbers, remove those terms which occupy positions which are
prime, leaving
{1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...}
; remove those terms whose positions are primes plus one; leaving
{1, 4, 9, 12, 15, 16, 18, ...}
; remove those whose positions are primes plus two; and so on...
What is the asymptotic behavior of this sequence? The Bojarincev asymptotic formula for the composite numbers allows a formula for
for any fixed
in terms of
. For example, the formula for
is
But is there a reasonable asymptotic for
without using earlier values?