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a(n) = prime(3*n+1) - prime(3*n-1).
4

%I #17 Jul 28 2020 16:31:18

%S 4,6,10,10,10,8,8,14,6,18,8,8,10,12,6,16,10,16,8,6,18,18,12,14,10,12,

%T 12,8,14,6,12,10,20,16,8,12,12,14,6,8,10,18,14,12,12,24,12,6,18,18,6,

%U 12,12,20,12,18,8,8,12,24,6,14,28,18,12,16,8,22,6,8,6,8,12,28,6,14,8,12,6,24

%N a(n) = prime(3*n+1) - prime(3*n-1).

%C Previous name was: Partition the primes in triples starting with 3: {3, 5, 7}, {11, 13, 17}, {19, 23, 29}, {31, 37, 41}, {43, 47, 53}, {59, 61, 67}, {71, 73, 79}, {83, 89, 97}, {101, 103, 107}. Sequence gives differences between smallest and largest prime in each triple.

%C Minimal difference is 6 (for 3-tuplet) except first triple. Repeating 6 means successive 3-tuplets, see A088683, A088684, ...

%t Table[Prime[3n+1]-Prime[3n-1],{n,80}] (* _Harvey P. Dale_, Jul 28 2020 *)

%o (PARI) a(n) = prime(3*n+1) - prime(3*n-1); \\ _Michel Marcus_, Oct 05 2013

%Y Cf. A088680, A078584, A088683, A088684.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Oct 05 2003

%E New name from _Michel Marcus_, Oct 05 2013