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%I #13 Nov 20 2021 21:10:29
%S 58,125,305,521,953,1313,1961,2833,3757,5317,6553,8081,9593,11425,
%T 14045,16477,19597,21913,24641,27829,30577,35113,40321,45509,50201,
%U 53873,56393,60281,68465,75665,86857,91669,101117,106301
%N a(n) = (prime(n) + prime(n+2))^2 + prime(n+1)^2.
%C 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.
%F a(n) = prime(n)^2 + prime(n+1)^2 + prime(n+2)^2 + 2*prime(n)*prime(n+2).
%e For n = 1 the a(1) = (prime(1) + prime(3))^2 + prime(2)^2 = (2 + 5)^2 + 3^2 = 49 + 9 = 58.
%t Table[(Prime[n] + Prime[n + 2])^2 + Prime[n + 1]^2,{n,34}]
%Y Cf. A000040, A090076, A133529.
%K nonn,easy
%O 1,1
%A _Burak Muslu_, Oct 23 2021