A226939 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.

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, 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, 17, 10, 17, 10, 10, 54, 54, 4, 14, 14, 14, 8, 8, 8

Offset

1,3

Comments

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Example

a(n) values frequently depend on both lesser and higher terms:
a(3)= 1+ min( a(C(3)), a(C(C(3)))) = 4
a(3)= 1+ min( a(10), a(5))= 1+min(4,3) = 4
a(10)=1+ min( a(5), a(16))= 1+min(3,3) = 4
a(5) =1+ min( a(16),a(8)) = 1+min(3,2) = 3
a(16)=1+ min( a(8), a(4)) = 1+min(2,2) = 3
a(8) =1+ min( a(4), a(2)) = 1+min(1,1) = 2
a(4) =1+ min( a(2), a(1)) = 1+min(1,1) = 2
a(2) =1 (starting value)

Prog

(PARI) C(n)=if(n%2, 3*n+1, n/2)
A=vector(10^4); A[1]=A[2]=1;
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
(Blitz3D) function A(n)
            if n=1 or 2
                   return 1
            else
                   return 1 +lesser(A(C(n)), A(C(C(n))))
            end if
end function
; The Collatz Sequence generator equation
Function C(n)
       If n Mod 2
                 Return 3*n+1
       Else
                 Return n Shr 1
       End If
End Function
;; Andres M. Torres, Jun 26 2013

Crossrefs

Cf. A014682.

Sequence in context: A010646 A284307 A160079 * A123403 A276957 A275847

Adjacent sequences: A226936 A226937 A226938 * A226940 A226941 A226942

Keyword

nonn

Author

Andres M. Torres, Jun 22 2013

Status

approved