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A222582
Smallest numbers k such that A006577(n+k) = A006577(n) + A006577(k), or 0 if no such number exists.
0
12, 2, 0, 0, 1152, 24, 26, 22, 16, 12, 0, 10, 10, 0, 10, 9, 0, 0, 0, 0, 0, 8, 0, 6, 8, 7, 6094, 8, 8, 8, 456, 8, 6, 249, 268, 133, 6, 131, 120, 6, 301, 7, 96, 6, 6, 112, 0, 79, 74, 77, 6, 6, 86, 0, 0, 67, 70, 65, 68, 6, 6, 84, 84, 6, 58, 61, 56, 6, 66, 6, 58
OFFSET
1,1
COMMENTS
A006577 is the number of halving and tripling steps to reach 1 in '3x+1' problem.
a(n) = 0 for n = 3, 4, 11, 14, 17, 18, 19, 20, 21, 23, 47, 54, 55, 73, ...
EXAMPLE
a(12)=10 because A006577(12+10) = 15, and A006577(12) + A006577(10) = 9 + 6 = 15.
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 n from 1 to 73 do: ii:=0:for k from 2 to 100000 while(ii=0) do:z:=n+k : if C(z)=C(n)+C(k) then ii:=1: printf ( "%d %d \n", n, k):else fi:od: if ii=0 then printf ( "%d %d \n", n, 0):else fi:od:
CROSSREFS
Sequence in context: A157780 A223514 A232627 * A260621 A264024 A010204
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 25 2013
STATUS
approved