Intended for: September 6, 2013
Timetable
- First draft entered by Alonso del Arte on September 3, 2011 ✓
- Draft reviewed by Daniel Forgues on September 5, 2011 ✓
- Draft to be approved by August 6, 2011
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A066888: Number of
primes between the
th triangular number (exclusive) and the next (inclusive):
π (Tn +1 ) − π (Tn ), n ≥ 0 |
.
-
{ 0, 2, 1, 1, 2, 2, 1, 2, 3, 2, ... }
Triangle begins
1 (0 prime in (T_0, T_1])
2 3 (2 primes in (T_1, T_2])
4 5 6 (1 prime in (T_2, T_3])
7 8 9 10 (1 prime in (T_3, T_4])
11 12 13 14 15 (2 primes in (T_4, T_5])
It is believed that the initial zero of this sequence is the only zero in the sequence. That is to say, that there is always a prime in
for
. (Or there is always a positive
noncomposite for
, since
1 is a
unit.) (With the exception of
1 and
3, all triangular numbers are composite, since
.)