A350370 a(n) is the smallest k such that the Collatz sequence for k includes a record number of consecutive tripling steps.

1, 3, 7, 15, 27, 127, 255, 511, 1023, 1819, 4095, 4255, 16383, 32767, 65535, 77671, 262143, 459759, 1048575, 2097151, 4194303, 7456539, 16777215, 33554431, 67108863, 125687199, 1073741823, 2147483647, 4294967295, 8589934591, 17179869183, 20361326439, 68719476735

Offset: 1

Author

Kevin P. Thompson, Dec 27 2021

Keywords

• nonn

Comments

See A350369 for a description of "consecutive tripling steps."

Records for A350369, recorded by the Collatz sequence starting value.

Differs from A213215 in that repeated values are removed, i.e., if a gap in the number of consecutive tripling steps occurs, A213215 will report the starting value multiple times but this sequence will not. Example: The Collatz sequence for 15 has 4 tripling steps but the sequence for 27 has 6, so 27 is reported by A213215 for n=5 and n=6. This sequence only reports 27 once as having set a new record.

Differs from A222598 in that certain consecutive tripling step lengths will not be represented here when a gap in the record number of consecutive tripling steps occurs. Example: Since the consecutive tripling step record moves from 4 in the Collatz sequence for 15 to 6 in the Collatz sequence for 27, this sequence will not report the Collatz sequence for 159 with 5 consecutive tripling steps like A222598 does.

Examples

			a(5) = 27 since the Collatz sequence for 27 is the 5th sequence to set a record for the most consecutive tripling steps, i.e., A350369(27) = 6 is the first occurrence of 6 in A350369.
		

Links

• Kevin P. Thompson, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A006370, A213215, A222598, A347270, A347668, A350369.

Programs

Mathematica

k=0;nmax=0;Do[While[t=0;max=0;NestWhileList[If[OddQ@#,t++;If[t>max,max=t];(3#+1)/2,t=0;#/2]&,++k,#!=1&];maxGiorgos Kalogeropoulos, Jan 11 2022 *)