A222582 Smallest numbers k such that A006577(n+k) = A006577(n) + A006577(k), or 0 if no such number exists.

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, ...

Links

Table of n, a(n) for n=1..71.

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

Cf. A006577, A221947.

Sequence in context: A157780 A223514 A232627 * A260621 A264024 A010204

Adjacent sequences: A222579 A222580 A222581 * A222583 A222584 A222585

Keyword

nonn

Author

Michel Lagneau, Feb 25 2013

Status

approved