A226939 - OEIS

%I #23 Sep 26 2015 13:18:56

%S 1,1,4,2,3,5,9,2,10,4,8,5,5,9,9,3,7,11,11,4,4,8,8,6,12,6,56,10,10,10,

%T 54,3,14,7,7,11,11,11,18,5,55,5,15,9,9,9,53,6,13,13,13,6,6,57,57,10,

%U 17,10,17,10,10,54,54,4,14,14,14,8,8,8

%N A recursive variation of the Collatz-Fibonacci sequence: a(n) = 1 + min(a(C(n)),a(C(C(n)))) where C(n) = A006370(n), the Collatz map.

%C The sequence contains mysterious duplicates of terms, sometimes in groups of 2 to 4 at a time, but I haven't seen any cyclic patterns, it's all unique.

%H Charles R Greathouse IV, <a href="/A226939/b226939.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 1 + min(a(C(n)), a(C(C(n)))), where C(n) = A006370(n).

%e a(n) values frequently depend on both lesser and higher terms:

%e a(3)= 1+ min( a(C(3)), a(C(C(3)))) = 4

%e a(3)= 1+ min( a(10), a(5))= 1+min(4,3) = 4

%e a(10)=1+ min( a(5), a(16))= 1+min(3,3) = 4

%e a(5) =1+ min( a(16),a(8)) = 1+min(3,2) = 3

%e a(16)=1+ min( a(8), a(4)) = 1+min(2,2) = 3

%e a(8) =1+ min( a(4), a(2)) = 1+min(1,1) = 2

%e a(4) =1+ min( a(2), a(1)) = 1+min(1,1) = 2

%e a(2) =1 (starting value)

%o (PARI) C(n)=if(n%2,3*n+1,n/2)

%o A=vector(10^4);A[1]=A[2]=1;

%o a(n)=if(n<=#A && A[n], A[n], my(c=C(n),t=min(a(c), a(C(c)))+1); if(n>#A, t, A[n]=t)) \\ _Charles R Greathouse IV_, Jun 24 2013

%o (Blitz3D) function A(n)

%o             if n=1 or 2

%o                    return 1

%o             else

%o                    return 1 +lesser(A(C(n)), A(C(C(n))))

%o             end if

%o end function

%o ; The Collatz Sequence generator equation

%o Function C(n)

%o        If n Mod 2

%o                  Return 3*n+1

%o        Else

%o                  Return n Shr 1

%o        End If

%o End Function

%o ;; _Andres M. Torres_, Jun 26 2013

%Y Cf. A014682.

%K nonn

%O 1,3

%A _Andres M. Torres_, Jun 22 2013