The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356462

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A356462

a(n) is the maximum number of Z x Z lattice points inside or on a circle of radius n^(1/2) for any position of the center of the circle.
(history; published version)

#20 by Michael De Vlieger at Sat Aug 13 15:45:59 EDT 2022

STATUS

reviewed

approved

#19 by Hugo Pfoertner at Sat Aug 13 14:18:24 EDT 2022

STATUS

proposed

reviewed

#18 by Jon E. Schoenfield at Tue Aug 09 22:29:13 EDT 2022

STATUS

editing

proposed

#17 by Jon E. Schoenfield at Tue Aug 09 22:29:07 EDT 2022

COMMENTS

The terms of square index of this sequence are such that a(n^2) = A123690(2n), e.g. , a(9) = 32 = A123690(6).

FORMULA

Let N(u,v,n) be the number of integer solutions (x,y) of (x-u)^2 + (y-v)^2 <= n. Then a(n) is the maximum of N(u,v,n) taken over 0 <= u <= 1/2 and 0 <= v <= u. The symetries of the square lattice allow to limit the domain of the circle center (u,v) to this triangle. The terms of this sequence were found by '"brute force' " search of the maximum of N(u,v,n) for (u,v) in this triangular domain.

STATUS

proposed

editing

#16 by Bernard Montaron at Tue Aug 09 11:14:17 EDT 2022

STATUS

editing

proposed

#15 by Bernard Montaron at Tue Aug 09 11:14:11 EDT 2022

COMMENTS

The terms of square index of this sequence are such that a(n^2) = A123690(2n), e.g. a(9) = 26 32 = A123690(6).

STATUS

proposed

editing

#14 by Omar E. Pol at Tue Aug 09 11:11:22 EDT 2022

STATUS

editing

proposed

Discussion

Tue Aug 09

11:12

Bernard Montaron: In "COMMENTS" the number '26' needs to be changed to '32'. Somehow, the edit does not take it...

#13 by Omar E. Pol at Tue Aug 09 11:11:19 EDT 2022

COMMENTS

a(n) >= A057655(n).

a(n) >= A057655(n). The terms of square index of this sequence are such that a(n^2) = A123690(2n) , , e.g. a(9) = 26 = A123690(6).

EXAMPLE

For n = 1 the maximum number of Z x Z lattice points inside the circle is a(1) = 5. The maximum is obtained with the circle centered at x = 0, y = 0.

STATUS

proposed

editing

#12 by Bernard Montaron at Tue Aug 09 11:09:52 EDT 2022

STATUS

editing

proposed

#11 by Bernard Montaron at Tue Aug 09 11:09:00 EDT 2022

COMMENTS

a(n) >= A057655(n). The terms of square index of this sequence are such that a(n^2) = A123690(2n) , e.g. a(9)=26=A123690(6).

CROSSREFS

Cf. A057655, A123690, A346993.

STATUS

proposed

editing

Discussion

Tue Aug 09

11:09

Bernard Montaron: Indeed, A346993 is a very interesting sequence!