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A221947 Smallest number k (different from a power of 2) such that A006577(n*k) = A006577(n) + A006577(k), or 0 if no such number exists. 1
3, 3, 423, 3, 81, 423, 75, 3, 0, 81, 11003, 423, 155, 75, 35, 3, 239, 0, 151, 81, 23, 11003, 21, 423, 21, 155, 341, 75, 201, 35, 75, 3, 21, 239, 15, 0, 113, 151, 21, 81, 635, 23, 1131, 11003, 2017, 21, 75, 423, 1267, 21, 75, 155, 253, 341, 151, 75, 7931, 201, 75, 35, 69, 75, 213, 3, 1073, 21, 423, 239, 61, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A006577 is the number of halving and tripling steps to reach 1 in the '3x+1' problem. If n is a power of 2, a(n) = 3.

If k is a power of 2, we obtain trivial results, for example A006577(n*2^m) = A006577(2^m) + A006577(n) = m + A006577(n) => the smallest k is 1.

It appears that a(n) = 0 for n of the form 9*2^a = 9, 18, 36, 72, ...

LINKS

Table of n, a(n) for n=1..70.

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

EXAMPLE

a(3) = 423 because A006577(3*423) = A006577(1269) = 39, and A006577(3) + A006577(423) = 7 + 32 = 39.

MAPLE

lst:={ }:C:= proc(n) a := 0 ; x := n ; while x > 1 do if type(x, 'even') then x := x/2:a:=a+1:  else x := 3*x+1 ; a := a+1 ; end if; end do; a ; end proc:

for m from 0 to 40 do:lst:=lst union {2^m}:od:for n from 1 to 73 do: ii:=0:for k from 2 to 50000 while(ii=0) do:z:=n*k : if {k} intersect lst = {} and C(z)=C(n)+C(k) then ii:=1: printf ( "%d %d \n", n, k):else fi:od: if ii=0 and {n} intersect lst = {} and {k} intersect lst = {} then printf ( "%d %d \n", n, 0):else fi:od:

CROSSREFS

Cf. A006577, A057716.

Sequence in context: A335258 A292163 A242886 * A138662 A009011 A291095

Adjacent sequences:  A221944 A221945 A221946 * A221948 A221949 A221950

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 25 2013

STATUS

approved

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)