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A281938 a(n) is the least k such that gcd(A006666(k), A006667(k)) = n. 1
2, 4, 8, 16, 32, 64, 128, 256, 512, 82, 129, 4096, 327, 16384, 32768, 1249, 35655, 159, 4926, 283, 377, 502, 603, 799, 1063, 1417, 1889, 2518, 3356, 4472, 5960, 7944, 10594, 14124, 18833, 25110, 33481, 44641, 59521, 79361, 105814, 141084, 188113, 250817, 334422 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A006666: Number of halving steps to reach 1 in '3x+1' problem.

A006667: number of tripling steps to reach 1 in '3x+1' problem.

a(n) = 2^n for n = 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 12, 14, 15.

The primes in the sequence are 2, 283, 1063, 1249, 1889, 44641, ...

LINKS

Table of n, a(n) for n=1..45.

Index entries for sequences related to 3x+1 (or Collatz) problem

EXAMPLE

a(10) = 82 because gcd(A006666(82), A006667(82)) = gcd(70, 40) = 10, and there is no k < 82 such that gcd(A006666(k), A006667(k)) = 10.

MAPLE

for n from 1 to 45 do:

ii:=0:

for k from 2 to 10^7 while(ii=0) do:

  m:=k:s1:=0:s2:=0:

   for i from 1 to nn while(m<>1) do:

    if irem(m, 2)=0

     then

     s2:=s2+1:m:=m/2:

     else

     s1:=s1+1:m:=3*m+1:

    fi:

   od:

    if gcd(s1, s2)=n

     then

     ii:=1:printf(`%d %d \n`, n, k):

     else

    fi:

od:

od:

MATHEMATICA

Function[w, First /@ Lookup[w, Function[k, If[k == {}, #, Take[#, First@ k]]]@ Complement[Range@ Max@ #, #]] &@ Keys@ w]@ KeySort@ PositionIndex@ Table[GCD[Count[NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &], _?(EvenQ[#] &)], Count[Differences[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]], _?Positive]], {n, 2^16}] (* Michael De Vlieger, Feb 02 2017, Version 10, after Harvey P. Dale at A006666 and A006667 *)

CROSSREFS

Cf. A006577, A006666, A006667.

Sequence in context: A126605 A072067 A072049 * A242350 A115213 A009714

Adjacent sequences:  A281935 A281936 A281937 * A281939 A281940 A281941

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 02 2017

STATUS

approved

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Last modified June 15 13:25 EDT 2021. Contains 345048 sequences. (Running on oeis4.)