A324249 Dropping times (A122458) exceeding 5 for odd numbers under reduced Collatz iteration corresponding to A324248.

37, 35, 34, 34, 32, 28, 26, 19, 9, 25, 13, 18, 8, 8, 19, 7, 12, 17, 8, 15, 6, 8, 13, 13, 6, 10, 6, 7, 9, 9, 6, 25, 7, 10, 12, 17, 6, 11, 8, 8, 10, 6, 6, 10, 7, 8, 14, 15, 24, 8, 51, 8, 6, 15, 13, 12, 10, 17, 8

Offset: 1

Author

Wolfdieter Lang, Feb 21 2019

Keywords

• nonn

Comments

The odd numbers with dropping time >= 6 under reduced Collatz iteration are given in A324248. Note that the dropping times do not follow the modulo 256 pattern of A324248.

Note that the Collatz conjecture is assumed. Otherwise there may exist (very large) odd numbers for which no finite dropping time exists.

Examples

			a(1) = 37 for A324248(1) = 27, but a(20) = 15 for A324248(20) = 283 == 27 (mod 256) (no mod 256 pattern).
		

References

• Victor Klee and Stan Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory, Mathematical Association of America (1991) pp. 191-194, 225-229, 308-309.

Crossrefs

Cf. A122458, A324248.

Formula

a(n) = A122458((A324248(n) - 1)/2), for n >= 1.