A360734 The number of regions into which the plane is divided by a hypotrochoid with parameters R = d = prime(n+1) and r = prime(n).

2, 7, 9, 35, 15, 53, 21, 71, 147, 33, 187, 125, 45, 143, 267, 297, 63, 337, 215, 75, 397, 251, 447, 681, 305, 105, 323, 111, 341, 1653, 395, 687, 141, 1343, 153, 787, 817, 503, 867, 897, 183, 1721, 195, 593, 201, 2323, 2455, 683, 231, 701, 1197

Offset

1,1

Comments

The hypotrochoid is given by three parameters: R is the radius of the fixed circle, r is the radius of the rotating disk, d is the distance from the "drawing" point of the disk to the center of this disk.

Links

Table of n, a(n) for n=1..51.

Nicolay Avilov, Illustration for terms a(1) - a(10) of the sequence

Formula

a(n) = prime(n+1)*(prime(n+1) - prime(n) - 1) + 2.

Example

See illustration in Links.
a(4) = 11*(11 - 7 - 1) + 2 = 35.

Mathematica

a[n_]:=Prime[n+1]*(Prime[n+1] - Prime[n]- 1) + 2; Array[a, 51] (* Stefano Spezia, Feb 18 2023 *)

Crossrefs

Cf. A000040.

Sequence in context: A126871 A125770 A042063 * A041717 A002353 A041073

Adjacent sequences: A360731 A360732 A360733 * A360735 A360736 A360737

Keyword

nonn

Author

Nicolay Avilov, Feb 18 2023

Status

approved