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A220492
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Number of primes p between quarter-squares, Q(n) < p <= Q(n+1), where Q(n) = A002620(n).
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5
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0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 4, 3, 1, 4, 2, 4, 3, 3, 3, 4, 4, 3, 4, 3, 2, 4, 4, 5, 4, 4, 4, 3, 4, 4, 4, 5, 4, 4, 4, 4, 5, 5, 5, 4, 6, 4, 4, 5, 5, 5, 7, 2, 3, 6, 6, 6, 6, 5, 8, 4, 5, 6, 5, 4, 7
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OFFSET
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0,9
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COMMENTS
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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
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LINKS
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EXAMPLE
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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):
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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
...
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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