A368241 a(n) = n - prevprime(n) if n is prime, n + primepi(n) otherwise; a(2) = 2.

1, 2, 1, 6, 2, 9, 2, 12, 13, 14, 4, 17, 2, 20, 21, 22, 4, 25, 2, 28, 29, 30, 4, 33, 34, 35, 36, 37, 6, 40, 2, 43, 44, 45, 46, 47, 6, 50, 51, 52, 4, 55, 2, 58, 59, 60, 4, 63, 64, 65, 66, 67, 6, 70, 71, 72, 73, 74, 6, 77, 2, 80, 81, 82, 83, 84, 6, 87, 88, 89, 4, 92, 2, 95, 96

Offset: 1

Author

Hendrik Kuipers, Dec 18 2023

Keywords

• nonn
• easy

Comments

prevprime(n) = A151799(n) is the largest prime < n.

a(n) = 2 iff n=2 or n is the larger prime of a twin prime pair (A006512).

Crossrefs

Cf. A000720, A005171, A010051, A006512, A095117, A151799.

Cf. A368196 (trajectories).

Programs

Mathematica

Table[If[n<3, n, If[PrimeQ[n], n-NextPrime[n,-1], n+PrimePi[n]]],{n,75}] (* James C. McMahon, Dec 19 2023 *)

PARI

a(n) = if (isprime(n), n - precprime(n-1), n + primepi(n)); \\ Michel Marcus, Dec 18 2023