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A220492 Number of primes p between quarter-squares, Q(n) < p <= Q(n+1), where Q(n) = A002620(n). 4
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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..86.

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)

---------------------------------------

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

...

CROSSREFS

Partial sums give A220506.

Cf. A000040, A002620, A001477, A014085, A066888, A073882, A222030.

Sequence in context: A037226 A089641 A086995 * A229873 A135230 A117957

Adjacent sequences:  A220489 A220490 A220491 * A220493 A220494 A220495

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 04 2013

STATUS

approved

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Last modified October 19 09:28 EDT 2018. Contains 316339 sequences. (Running on oeis4.)