A361826 a(n) is equal to the number of roots of the equation n*cos(x) = sqrt(x).

1, 1, 3, 5, 7, 11, 15, 21, 25, 31, 39, 45, 53, 63, 71, 81, 91, 103, 115, 127, 141, 155, 169, 183, 199, 215, 233, 249, 267, 287, 305, 325, 347, 367, 389, 413, 435, 459, 485, 509, 535, 561, 589, 617, 645, 673, 703, 733, 765, 795, 827, 861, 895, 929, 963, 999, 1035

Offset

1,3

Comments

The number of roots of the equation is determined graphically. It is equal to the number of intersection points of two graphs: y = n*cos(x) and y = sqrt(x).

Links

Table of n, a(n) for n=1..57.

Nicolay Avilov, Illustration for a(4).

Formula

Conjecture: a(n) = 2*floor(n^2/(2*Pi)) + 1.

Example

a(4) = 5 because the equation 4*cos(x) = sqrt(x) has 5 roots. See link.

Crossrefs

Cf. A178832.

Sequence in context: A194602 A337217 A333380 * A177139 A252793 A351924

Adjacent sequences: A361823 A361824 A361825 * A361827 A361828 A361829

Keyword

nonn

Author

Nicolay Avilov, Mar 27 2023

Status

approved