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A350370
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a(n) is the smallest k such that the Collatz sequence for k includes a record number of consecutive tripling steps.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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&]; max<nmax]; nmax=max+1; Print@k, 30] (* Giorgos Kalogeropoulos, Jan 11 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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