login
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
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
KEYWORD
nonn
AUTHOR
Andres M. Torres, Jun 22 2013
STATUS
approved