A336992 The number of gaps in 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, 0, 1, 3, 3, 9, 9, 8, 12, 12, 14, 15, 15, 16, 100, 99, 100, 100, 101, 108, 108, 112, 111, 110, 110, 110, 110, 111, 110, 116, 115, 115, 115, 116, 120, 120, 124, 123, 122, 122, 121, 122, 122, 123, 125, 124, 125, 125, 126, 125, 125, 127, 127, 126, 133, 133

Offset

0,4

Comments

The number of gaps would be relevant for sparse representations of the sets A(n), which may be of use for a numerical verification of the Collatz conjecture up to a given number.

Links

Markus Sigg, Table of n, a(n) for n = 0..999

Prog

(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; };
nGaps(A) = { my(i, c=0); for (i=2, #A, if (A[i-1] < A[i]-1, c = c+1; )); c; };
makeVec(m) = { my(v = [], A = Set([]), i); for(i = 1, m, v = concat(v, nGaps(A)); if (i < m, A = iter(A))); v; };
makeVec(57)

Crossrefs

Cf. A061641, A336938.

Sequence in context: A201456 A372267 A347033 * A349673 A064235 A098355

Adjacent sequences: A336989 A336990 A336991 * A336993 A336994 A336995

Keyword

nonn

Author

Markus Sigg, Aug 10 2020

Status

approved