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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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A143129 A185731 A177765 * A282068 A281843 A282225 Adjacent sequences:  A337119 A337120 A337121 * A337123 A337124 A337125 KEYWORD nonn AUTHOR Markus Sigg, Aug 17 2020 STATUS approved

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Last modified May 13 00:11 EDT 2021. Contains 343829 sequences. (Running on oeis4.)