A368690 Number of terms in the trajectory from n to 2 of the map x -> A368241(x), or -1 if n never reaches 2.

5, 2, 4, 2, 8, 3, 9, 6, 7, 2, 8, 7, 10, 6, 9, 2, 7, 6, 9, 6, 17, 8, 16, 8, 6, 5, 8, 2, 3, 16, 7, 15, 7, 5, 9, 10, 7, 6, 8, 2, 15, 6, 14, 6, 5, 10, 8, 9, 6, 5, 7, 7, 16, 3, 14, 5, 13, 2, 14, 4, 9, 7, 8, 5, 5, 13, 6, 6, 15, 2, 13, 11, 10, 12, 28, 5, 13, 3, 8, 6, 7, 15, 3, 4, 12, 5

Offset: 4

Author

Hendrik Kuipers, Jan 03 2024

Keywords

• nonn

Comments

It is conjectured that every starting n reaches 2 eventually.

A368241(x) decreases to the prime gap x-prevprime(x) when x is prime, or increases to x+primepi(x) otherwise, and will reach 2 when x is the greater of a twin prime pair (A006512, preceding prime gap 2).

Prime gaps and x+primepi(x) may become large, but if the twin prime conjecture is true then there would be large twin primes they might reach too.

Examples

			For n=4 the trajectory is 4 -> 6 -> 9 -> 13 -> 2 (row 4 of A368196) which has a(4) = 5 terms.
		

Crossrefs

Cf. A368241.

Cf. A000720, A005171, A010051, A006512.

Programs

PARI

f(n) = if (isprime(n), n - precprime(n-1), n + primepi(n)); \\ A368241
a(n) = my(k=1); while ((n = f(n)) != 2, k++); k+1; \\ Michel Marcus, Jan 03 2024