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 A232870 Numbers that are the largest value in the Collatz (3x+1) trajectories of exactly three initial values. 3
 40, 64, 100, 112, 136, 148, 184, 208, 244, 256, 280, 352, 400, 424, 472, 532, 544, 616, 640, 688, 712, 724, 784, 820, 832, 868, 904, 928, 964, 976, 1048, 1072, 1108, 1120, 1156, 1192, 1216, 1264, 1300, 1360, 1396, 1408, 1432, 1480, 1540, 1576, 1588, 1624, 1684 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that appear exactly 3 times in A025586, which gives the largest value in the 3x + 1 trajectory of n. For each term k in this sequence, the three initial values, that is, values of n at which A025586(n) = k, are (in ascending order) n1 = (k-1)/3, n2 = 2*n1 = 2*(k-1)/3, and n3 = k. n1 is the odd number from which an upward (that is, 3x + 1) step lands at k = 3*n1 + 1. It cannot be the case that n1 = 3 (mod 4), because we would then have k = 10 (mod 12), so k/2 would be odd, and its successor in the trajectory would be 3*k/2 + 1 > k, so k would not be the largest value in the trajectory. Thus, n1 = 1 (mod 4), so n2 = 2 (mod 8) and n3 = 4 (mod 12). Numbers that are the largest value in the 3x + 1 trajectory of exactly one initial value (that is, numbers that appear exactly once in A025586) are in A222562. Numbers that are not the largest value in the 3x + 1 trajectory of any initial value (that is, numbers that do not appear at all in A025586) are in A213199. LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 EXAMPLE 40 is in the sequence because it is the largest value in the 3x + 1 trajectories of exactly three initial values: 13, 26, and 40 itself. The trajectories are as follows: ..... 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 ........... 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 CROSSREFS Cf. A025586, A213199, A222562, A233293. Sequence in context: A204754 A204747 A205066 * A338373 A355778 A235283 Adjacent sequences: A232867 A232868 A232869 * A232871 A232872 A232873 KEYWORD nonn AUTHOR Jon E. Schoenfield, Dec 01 2013 STATUS approved

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Last modified September 26 14:15 EDT 2023. Contains 365660 sequences. (Running on oeis4.)