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%I #42 Nov 25 2024 09:08:43
%S 2,6,20,42,96,138,218,264,348,490,582,762,884,962,1086,1282,1510,1564,
%T 1890,2028,2110,2348,2570,2798,3128,3396,3528,3686,3798,3932,4672,
%U 4884,5096,5316,5802,5946,6274,6640,6850,7190,7464,7632,8166,8290,8538,8642,9334,10334,10520,10650,10830,11048,11240,11872,12088,12508
%N a(n) = prime(prime(prime(n))) - prime(prime(n)).
%F a(n) = A168152(prime(n)) = A014689(prime(prime(n))).
%F a(n) = A038580(n) - A006450(n).
%F a(n) ~ n*(log(n))^3.
%F a(n) == 0 (mod 2).
%e For n=5, A038580(5)=127 and A006450(5)=31 so a(5) = 127 - 31 = 96.
%p a:= ithprime@@3-ithprime@@2:
%p seq(a(n), n=1..56); # _Alois P. Heinz_, Nov 18 2024
%t Nest[Prime, Range[100], 3] - PrimePi /@ Nest[Prime, Range[100], 3]
%o (PARI) a(n) = my(q=prime(prime(n))); prime(q) - q; \\ _Michel Marcus_, Nov 18 2024
%Y Cf. A000040, A006450, A038580, A014689, A168152.
%K nonn,easy
%O 1,1
%A _Sean M. Drury_, Nov 17 2024