A341362 a(n) begins the first sequence of n consecutive positive integers with the same h-value and the same d-value in the Collatz (or '3x + 1') problem.

1, 54, 108, 290, 290, 386, 172146, 298200, 596400, 596400, 596400, 795201, 795201, 2849196, 2849196, 8965036, 33659819, 45529226, 52417676, 93186987, 104161282, 104161282, 104161282, 436089218, 436089218, 605581697, 934358530, 934358530, 934358530, 3826876112

Offset: 1

Author

Lamine Ngom, Feb 10 2021

Keywords

• nonn

Comments

The Collatz function is as follows: F(x) = x/2 if x is even, otherwise F(x) = 3*x+1.

It is conjectured that starting from any number, and repeatedly applying the function on its previous result, we will always reach 1.

The d-value (or flight duration, A006577) is the number of steps needed to reach 1. The h-value (or flight height, A025586) is the maximum of the number's trajectory.

Examples

			a(3) = 108 because 108, 109 and 110 have same d-value (113) and same h-value (9232).
And 108 is the smallest number starting such sequence of 3 consecutive positive integers with same d-value and same h-value.
		

Links

• Guo-Gang Gao, On consecutive numbers of the same height in the Collatz problem, Discrete Mathematics, Volume 112, pages 261-267, 1993.

Crossrefs

Cf. A078441, A277109, A268253, A006577 (duration), A025586 (height), A056959.