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Template:Sequence of the Day for September 6

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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
Yesterday's SOTD * Tomorrow's SOTD

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



A066888: Number of primes between the
n
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
(Tn , Tn +1]
for
n > 0
. (Or there is always a positive noncomposite for
n   ≥   0
, since 1 is a unit.) (With the exception of 1 and 3, all triangular numbers are composite, since
Tn =
n (n + 1)
2
.)