A378027 a(n) = prime(prime(prime(n))) - prime(prime(n)).

2, 6, 20, 42, 96, 138, 218, 264, 348, 490, 582, 762, 884, 962, 1086, 1282, 1510, 1564, 1890, 2028, 2110, 2348, 2570, 2798, 3128, 3396, 3528, 3686, 3798, 3932, 4672, 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

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A168152(prime(n)) = A014689(prime(prime(n))).

a(n) = A038580(n) - A006450(n).

a(n) ~ n*(log(n))^3.

a(n) == 0 (mod 2).

Example

For n=5, A038580(5)=127 and A006450(5)=31 so a(5) = 127 - 31 = 96.

Maple

a:= ithprime@@3-ithprime@@2:
seq(a(n), n=1..56);  # Alois P. Heinz, Nov 18 2024

Mathematica

Nest[Prime, Range[100], 3] - PrimePi /@ Nest[Prime, Range[100], 3]

Prog

(PARI) a(n) = my(q=prime(prime(n))); prime(q) - q; \\ Michel Marcus, Nov 18 2024

Crossrefs

Cf. A000040, A006450, A038580, A014689, A168152.

Sequence in context: A323724 A214307 A087134 * A383745 A370494 A036689

Adjacent sequences: A378024 A378025 A378026 * A378028 A378029 A378030

Keyword

nonn,easy

Author

Sean M. Drury, Nov 17 2024

Status

approved