cp's OEIS Frontend

A380609 Primes a single step away from a cycle under the mapping p-> gpf(2*p+1).

%I A380609 #23 Feb 16 2025 19:36:35
%S A380609 2,17,31,37,67,71,73,97,103,137,149,157,181,199,211,227,241,269,283,
%T A380609 313,337,367,379,409,487,541,563,577,587,607,617,643,661,769,787,857,
%U A380609 877,907,929,937,977,997,1039,1093,1151,1187,1237,1453,1543,1567,1579,1621
%N A380609 Primes a single step away from a cycle under the mapping p-> gpf(2*p+1).
%C A380609 The cycle that gets entered consists of the primes in A287865. It appears that the mapping p -> gpf(2*p+1) produces no other cycles.
%C A380609 Conjecture: under repeated mapping all primes ultimately enter the same cycle.
%e A380609 Prime 2 is in the sequence as it maps to 5. And so is 17 as it maps to 7.  The primes 3, 5, 7, 11, 13, 19, 23 and 47 are not included, as they are part of the cycle itself (and hence considered zero iterations away from the cycle).
%p A380609 gpf:= n -> max(numtheory:-factorset(n)):
%p A380609 filter:= proc(n) local S,t,x;
%p A380609   t:= gpf(2*n+1);
%p A380609   if t = n then return false fi;
%p A380609   S:= {n,t};
%p A380609   x:= t;
%p A380609   do
%p A380609     x:= gpf(2*x+1);
%p A380609     if member(x,S) then return (x = t) fi;
%p A380609     S:= S union {x};
%p A380609   od;
%p A380609 end proc:
%p A380609 select(filter, [seq(ithprime(i),i=1..1000)]); # _Robert Israel_, Feb 03 2025
%Y A380609 Cf. A006530, A076565, A287865.
%K A380609 nonn
%O A380609 1,1
%A A380609 _Johannes M.V.A. Koelman_, Jan 28 2025