A308480 a(n) = A000225(n) if n is prime, a(n) = A020639(n) otherwise.

3, 7, 2, 31, 2, 127, 2, 3, 2, 2047, 2, 8191, 2, 3, 2, 131071, 2, 524287, 2, 3, 2, 8388607, 2, 5, 2, 3, 2, 536870911, 2, 2147483647, 2, 3, 2, 5, 2, 137438953471, 2, 3, 2, 2199023255551, 2, 8796093022207, 2, 3, 2, 140737488355327, 2, 7, 2, 3, 2, 9007199254740991

Offset: 2

Author

Felix Fröhlich, May 30 2019

Keywords

• nonn

Comments

What is the asymptotic behavior of the sequences defined by the recursive map x -> a(x)? Do these sequences increase without bound or do they enter a repeating cycle?

For example, the trajectory of 11 under the above map starts 11, 2047, 23, 8388607, 47, 140737488355327, 2351, s, 4703, t, ..., where s is a 708-digit number and t is a 1416-digit number. t has no prime factor less than 2^64 (cf. GIMPS link).

Links

• GIMPS, PrimeNet Exponent Status for M4703

Crossrefs

Cf. A000225, A006370, A020639.

Programs

PARI

a(n) = if(ispseudoprime(n), 2^n-1, factor(n)[1, 1])