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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.

%I A337122 #15 Aug 18 2020 05:43:08
%S A337122 5,4,17,5,17,17,53,9,53,17,53,17,17,53,59,17,53,53,74,17,18,53,59,25,
%T A337122 61,34,1829,53,74,59,1829,27,101,53,44,53,93,74,225,17,1829,18,163,53,
%U A337122 57,59,1829,39,77,61,95,53,34,1829,1829,57,197,74,225,89
%N 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.
%C A337122 1829 appears so often because the number 27 has a long orbit.
%H A337122 Markus Sigg, <a href="/A337122/b337122.txt">Table of n, a(n) for n = 1..10000</a>
%o A337122 (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); };
%o A337122 a(n) = { my(o = orbitSize(n, 0), k); for(k = 1, oo, if(orbitSize(n, k) == o, return(k))); };
%o A337122 makeVec(m) = { my(v = [], n); for(n = 1, m, v = concat(v, a(n))); return(v); };
%o A337122 makeVec(60)
%Y A337122 Cf. A294643.
%K A337122 nonn
%O A337122 1,1
%A A337122 _Markus Sigg_, Aug 17 2020