A336256 The cardinalities of the sets A(n), where A(0) is the empty set and A(n+1) is the union of A(n) and the Collatz orbit of the smallest natural number missing in A(n).

0, 1, 4, 9, 10, 20, 23, 24, 33, 34, 39, 42, 43, 46, 141, 142, 145, 146, 149, 161, 162, 170, 173, 174, 179, 180, 187, 190, 191, 204, 205, 208, 209, 212, 220, 221, 230, 231, 232, 239, 240, 243, 244, 247, 252, 253, 256, 257, 260, 261, 262, 267, 270, 271, 284, 285

Offset: 0

Author

Markus Sigg, Aug 08 2020

Keywords

• nonn

Crossrefs

Cf. A061641, A336938.

Programs

PARI

firstMiss(A) = { my(i); if(#A == 0 || A[1] > 0, return(0)); for(i = 1, A[#A] + 1, if(!setsearch(A,i), return(i))); };
iter(A) = { my(a = firstMiss(A)); while(!setsearch(A,a), A = setunion(A, Set([a])); a = if(a % 2, 3*a+1, a/2)); A; };
makeVec(m) = { my(v = [], A = Set([]), i); for(i = 1, m, v = concat(v, #A); if (i < m, A = iter(A))); v; };
makeVec(56)