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A376079
a(n) is the largest difference of adjacent elements in the sorted list of the Collatz trajectory elements of n.
1
1, 6, 2, 8, 6, 12, 4, 12, 6, 12, 4, 20, 12, 54, 8, 14, 12, 30, 6, 32, 12, 54, 8, 18, 14, 1944, 12, 36, 54, 1944, 16, 18, 12, 54, 12, 56, 30, 66, 20, 1944, 22, 48, 8, 68, 54, 1944, 24, 38, 18, 78, 14, 80, 1944, 1944, 12, 24, 30, 66, 54, 54, 1944, 1944, 32, 48, 12
OFFSET
2,2
COMMENTS
Trajectories end when they reach 1.
EXAMPLE
The trajectory of 3 is (3,10,5,16,8,4,2,1), the sorted list of the trajectory elements is (1,2,3,4,5,8,10,16), the list of differences is (1,1,1,1,3,2,6) with maximum 6, so a(3) = 6.
PROG
(PARI) a(n) = my(L = List([n])); while(n > 1, n = if(n % 2 == 0, n/2, 3*n + 1); listput(L, n)); listsort(L); vecmax(vector(#L - 1, i, L[i+1] - L[i]));
CROSSREFS
Cf. A220237 (sorted trajectory), A008908, A025586.
Sequence in context: A011331 A155687 A021618 * A085589 A259931 A333350
KEYWORD
nonn
AUTHOR
Markus Sigg, Sep 09 2024
STATUS
approved