A337673 a(n) is the sum of all positive integers whose Collatz orbit has length n.

0, 1, 2, 4, 8, 16, 37, 74, 172, 344, 786, 1572, 3538, 7206, 16252, 33112, 73762, 149967, 330107, 678610, 1498356, 3082302, 6742487, 13855154, 30122440, 62388962, 135783788, 281177482, 608402189, 1259151448, 2711432766, 5646008216, 12172417990, 25339969480, 54409676729, 113159496364

Offset: 0

Author

Markus Sigg, Sep 15 2020

Keywords

• nonn

Comments

a(n) >= 2^(n-1) as 2^(n-1) has orbit length n.

Examples

			a(6) = 5+32 = 37 as the positive integers whose Collatz orbit has length 6 are {5,32} - the orbit of 5 is 5,16,8,4,2,1, and the orbit of 32 is 32,16,8,4,2,1.
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A000975, A005186, A153772.

Equals row sums of triangles A088975 and A127824.

Programs

PARI

nextSet(s) = { my(s1 = Set([])); for(i = 1, #s, s1 = setunion(s1, Set([2*s[i]])); if (s[i] > 4 && (s[i]-1) % 3 == 0 && (s[i]-1)/3 % 2 == 1, s1 = setunion(s1, Set([(s[i]-1)/3]))); ); return(s1); }
a(n) = { my(s = Set([1])); for(k = 1, n, s = nextSet(s); ); return(sum(i=1,#s,s[i])); }

Extensions

More terms from David A. Corneth, Sep 15 2020