A337122 a(n) is the smallest positive integer k for which the mod-k Collatz orbit has the same length as the ordinary Collatz orbit.

5, 4, 17, 5, 17, 17, 53, 9, 53, 17, 53, 17, 17, 53, 59, 17, 53, 53, 74, 17, 18, 53, 59, 25, 61, 34, 1829, 53, 74, 59, 1829, 27, 101, 53, 44, 53, 93, 74, 225, 17, 1829, 18, 163, 53, 57, 59, 1829, 39, 77, 61, 95, 53, 34, 1829, 1829, 57, 197, 74, 225, 89

Offset

1,1

Comments

1829 appears so often because the number 27 has a long orbit.

Links

Markus Sigg, Table of n, a(n) for n = 1..10000

Prog

(PARI) orbitSize(n, k) = { my(S = Set([])); if (k, n = n % k); while(!setsearch(S, n), S = setunion(S, Set([n])); n = if(n % 2, 3*n+1, n/2); if(k, n = n % k); ); return(#S); };
a(n) = { my(o = orbitSize(n, 0), k); for(k = 1, oo, if(orbitSize(n, k) == o, return(k))); };
makeVec(m) = { my(v = [], n); for(n = 1, m, v = concat(v, a(n))); return(v); };
makeVec(60)

Crossrefs

Cf. A294643.

Sequence in context: A185731 A177765 A367965 * A282068 A281843 A282225

Adjacent sequences: A337119 A337120 A337121 * A337123 A337124 A337125

Keyword

nonn

Author

Markus Sigg, Aug 17 2020

Status

approved