A376079 a(n) is the largest difference of adjacent elements in the sorted list of the Collatz trajectory elements of n.

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.

Links

Markus Sigg, Table of n, a(n) for n = 2..10001

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

Adjacent sequences: A376076 A376077 A376078 * A376080 A376081 A376082

Keyword

nonn

Author

Markus Sigg, Sep 09 2024

Status

approved