A374847 - OEIS

%I #18 Jul 23 2024 20:40:58

%S 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,24,25,26,27,28,

%T 29,30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,50,51,52,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,70,71,72,73,74,76,78,80,81,82,84

%N Numbers k which can be written as k = r+s where r and s are elements of the Collatz trajectory of k.

%C A trajectory term can be used twice as r = s, so all even numbers are terms (trajectory first term k/2).

%C The odd terms, which become sparse with increasing size, form A374909.

%H Markus Sigg, <a href="/A374847/b374847.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 is a term because its Collatz trajectory is {2, 1} and 2 = 1+1.

%e 21 is not a term: its Collatz trajectory is T = { 21, 64, 32, 16, 8, 4, 2, 1 } and there are no r,s in T with 21 = r+s.

%o (PARI) is_A374847(k) = { my(T=List(),m=k); while(m>1,if(m%2==0,m=m/2,m=3*m+1); if(m<k,listput(T,m)););	for(i=1,#T,for(j=i,#T,if(T[i]+T[j]==k,return(1));)); return(0); }

%Y Cf. A374909.

%K nonn

%O 1,1

%A _Markus Sigg_, Jul 22 2024