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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 20 05:37 EDT 2019. Contains 325168 sequences. (Running on oeis4.)