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%I #22 Aug 02 2023 14:11:28
%S 2,7,3,17,7,29,11,41,13,17,67,79,23,89,29,29,31,127,137,37,149,163,43,
%T 47,197,53,211,59,223,59,257,67,71,281,79,307,317,331,89,89,97,367,97,
%U 389,101,401,431,449,127,461,127,127,487,127,131,137,137,547,557,149
%N a(n) = nextprime( p(n)/2 if p(n)=2 (mod 3), 2p(n) else ) = A007918( A138750( A000040( n ))).
%C 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.)
%C 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.
%C The sequence A124123 lists the primes which do not occur in the present sequence.
%C See A138750 for further information.
%H Paolo Xausa, <a href="/A138751/b138751.txt">Table of n, a(n) for n = 1..10000</a>
%H Georges Brougnard, <a href="https://www.echolalie.org/echolaliste/gbnums/gb0.jpg">Definition of GB-sequences</a>.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F a(n) = A007918(A138750(A000040(n))).
%e a(1) = nextprime(2/2) = 2, a(2) = nextprime(2*3) = 7, a(3) = nextprime(5/2) = 7.
%t A138751[n_]:=With[{p=Prime[n]},NextPrime[If[Mod[p,3]==2,p/2,2p]]];Array[A138751,100] (* _Paolo Xausa_, Jul 28 2023 *)
%o (PARI) A138751(n) = { n=prime(n); nextprime( if( n%3==2, ceil(n/2), 2*n ))}
%Y Cf. A124123, A007918, A138750, A138752-A138753.
%K easy,nonn
%O 1,1
%A _M. F. Hasler_, Mar 28 2008
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