A138751 a(n) = nextprime( p(n)/2 if p(n)=2 (mod 3), 2p(n) else ) = A007918( A138750( A000040( n ))).

2, 7, 3, 17, 7, 29, 11, 41, 13, 17, 67, 79, 23, 89, 29, 29, 31, 127, 137, 37, 149, 163, 43, 47, 197, 53, 211, 59, 223, 59, 257, 67, 71, 281, 79, 307, 317, 331, 89, 89, 97, 367, 97, 389, 101, 401, 431, 449, 127, 461, 127, 127, 487, 127, 131, 137, 137, 547, 557, 149

Offset: 1

Author

M. F. Hasler, Mar 28 2008

Keywords

• easy
• nonn

Comments

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.

Examples

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

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Georges Brougnard, Definition of GB-sequences.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

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

Programs

Mathematica

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 ))}

Formula

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