1,1

Composing the map A138750 with A007918 to the left and restricting it to the primes makes it a mapping from primes into primes which is a natural generalization of the Collatz problem to primes. (Looking at parity would not be interesting for primes, so using "mod 3" is the simplest nontrivial generalization.)

The only even prime p=2 is the only fixed point of this map and all odd primes seem to end up in the loop 7 -> 17 -> 11 -> 7, after a number of steps given in A138752.

The sequence A124123 lists the primes which do not occur in the present sequence.

See A138750 for further information.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Georges Brougnard, Definition of GB-sequences.

a(n) = A007918(A138750(A000040(n))).

a(1) = nextprime(2/2) = 2, a(2) = nextprime(2*3) = 7, a(3) = nextprime(5/2) = 7.

A138751[n_]:=With[{p=Prime[n]}, NextPrime[If[Mod[p, 3]==2, p/2, 2p]]]; Array[A138751, 100] (* Paolo Xausa, Jul 28 2023 *)

(PARI) A138751(n) = { n=prime(n); nextprime( if( n%3==2, ceil(n/2), 2*n ))}

Cf. A124123, A007918, A138750, A138752-A138753.

Sequence in context: A099130 A362359 A076992 * A112303 A336854 A209666

Adjacent sequences: A138748 A138749 A138750 * A138752 A138753 A138754

easy,nonn

M. F. Hasler, Mar 28 2008

approved