OFFSET
0,9
COMMENTS
It appears that a(n) > 0, if n > 1.
Apparently the above comment is equivalent to the Oppermann's conjecture. - Omar E. Pol, Oct 26 2013
For n > 0, also the number of primes per quarter revolution of the Ulam Spiral. The conjecture implies that there is at least one prime in every turn after the first. - Ruud H.G. van Tol, Jan 30 2024
LINKS
Ruud H.G. van Tol, Table of n, a(n) for n = 0..10000
Wikipedia, Oppermann's conjecture
EXAMPLE
When the nonnegative integers are written as an irregular triangle in which the right border gives the quarter-squares without repetitions, a(n) is the number of primes in the n-th row of triangle. See below (note that the prime numbers are in parenthesis):
---------------------------------------
Triangle a(n)
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0; 0
1; 0
(2); 1
(3), 4; 1
(5), 6; 1
(7), 8, 9; 1
10, (11), 12; 1
(13), 14, 15, 16; 1
(17), 18, (19), 20; 2
21, 22, (23), 24, 25; 1
26, 27, 28, (29), 30; 1
...
PROG
(PARI) a(n) = #primes([n^2/4, (n+1)^2/4]); \\ Ruud H.G. van Tol, Feb 01 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 04 2013
STATUS
approved