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

0,3

Comments

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

Links

Table of n, a(n) for n=0..35.

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

Example

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.

Prog

(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])); }

Crossrefs

Cf. A000975, A005186, A153772.

Equals row sums of triangles A088975 and A127824.

Sequence in context: A095236 A348847 A018536 * A162428 A344491 A028497

Adjacent sequences: A337670 A337671 A337672 * A337674 A337675 A337676

Keyword

nonn

Author

Markus Sigg, Sep 15 2020

Extensions

More terms from David A. Corneth, Sep 15 2020

Status

approved