

A222598


Least number k having Collatz (3x+1) sequence with exactly n pairs of odd and even numbers in a row.


2



5, 3, 7, 15, 159, 27, 127, 255, 511, 1023, 1819, 4095, 4255, 16383, 32767, 65535, 77671, 262143, 459759, 1048575, 2097151, 4194303, 7456539, 16777215, 33554431, 67108863, 134217727, 268435455, 125687199, 1073741823, 2147483647, 4294967295, 8589934591
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OFFSET

1,1


COMMENTS

This sequence is very similar to A213215. It is somewhat surprising that many of these numbers are of the form 2^k  1. Note that this is true for n = 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, and 33; not true for n = 1, 5, 6, 11, 13, 17, 19, 23, and 29.


LINKS



EXAMPLE

The Collatz sequence of 15 is 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1. It begins with 4 pairs of odd/even numbers.


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOnes[t_] := Module[{mx = 0, cnt = 0, i = 0}, While[i < Length[t], i++; If[t[[i]] == 1, cnt++; i++, If[cnt > mx, mx = cnt]; cnt = 0]]; mx]; nn = 15; t = Table[0, {nn}]; t[[1]] = 1; n = 1; While[Min[t] == 0, n = n + 2; c = countOnes[Mod[Collatz[n], 2]]; If[c <= nn && t[[c]] == 0, t[[c]] = n]]; t


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



