A348569 a(n) = (prime(n) + prime(n+2))^2 + prime(n+1)^2.

58, 125, 305, 521, 953, 1313, 1961, 2833, 3757, 5317, 6553, 8081, 9593, 11425, 14045, 16477, 19597, 21913, 24641, 27829, 30577, 35113, 40321, 45509, 50201, 53873, 56393, 60281, 68465, 75665, 86857, 91669, 101117, 106301

Offset: 1

Author

Burak Muslu, Oct 23 2021

Keywords

• nonn
• easy

Comments

The square of the shortest distance between the start and end points of the path followed by a person moving 90 degrees left and right (or left and right) at the end of each path on a path of three consecutive prime numbers.

Examples

			For n = 1 the a(1) = (prime(1) + prime(3))^2 + prime(2)^2 = (2 + 5)^2 + 3^2 = 49 + 9 = 58.
		

Crossrefs

Cf. A000040, A090076, A133529.

Programs

Mathematica

Table[(Prime[n] + Prime[n + 2])^2 + Prime[n + 1]^2,{n,34}]

Formula

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