A368690 - OEIS

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

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OFFSET

4,1

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.

LINKS

Table of n, a(n) for n=4..89.

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A368241.

Cf. A000720, A005171, A010051, A006512.

Sequence in context: A181696 A157121 A372286 * A083241 A111145 A249920

Adjacent sequences: A368687 A368688 A368689 * A368691 A368692 A368693

KEYWORD

nonn

AUTHOR

Hendrik Kuipers, Jan 03 2024

STATUS

approved