A064657 - OEIS

%I #26 Dec 05 2022 08:31:43

%S 1,1,1,1,2,4,8,12,10,5,2,2,13,12,26,13,3,9,14,11,11,25,12,26,13,13,27,

%T 27,26,4,2,6,34,10,60,5,28,53,22,62,25,24,22,25,22,51,38,25,28,3,26,

%U 53,16,53,27,63,26,4,10,12,86,57,42,79,24,36,25,38,56,32,85,23

%N a(n) = a(|n - a(n-3)|) + a(|n - a(n-4)|) for n > 3, a(n)=1 otherwise.

%C The sequence is defined only for n <= 866, see example. - _Reinhard Zumkeller_, Jul 21 2012

%H Reinhard Zumkeller, <a href="/A064657/b064657.txt">full Table of n, a(n) for n = 0..866</a>

%e Last term: a(866) = a(|866 - a(866-3)|) + a(|866 - a(866-4)|) = a(|866 - a(863)|) + a(|866 - a(862)|) = a(|866 - 718|) + a(|866 - 88|) = a(148) + a(778) = 28 + 655 = 683,

%e but a(867) = a(|867 - a(867-3)|) + a(|867 - a(867-4)|) = a(|867 - a(864)|) + a(|867 - a(863)|) =  a(|867 - 2546|) + a(|867 - 718|) = a(1679) + a(149) = undefined + 112 = undefined.

%o (Haskell)

%o a064657 n = a064657_list !! n

%o a064657_list = map fromJust $ takeWhile (/= Nothing) zs where

%o   z n = fromJust $ zs !! n

%o   zs = (map Just [1,1,1,1]) ++ f 4 where

%o      f x = y : f (x + 1) where

%o        y | 2*x < max i3 i4 = Nothing

%o          | otherwise       = Just $ z (abs (x - i3)) + z (abs (x - i4))

%o          where i3 = z (x - 3); i4 = z (x - 4)

%o b064657 = bFile' "A064657" a064657_list 0 -- (0.03 secs, 3184228 bytes)

%o -- _Reinhard Zumkeller_, Jul 21 2012

%o (PARI) A064657_vec=[1,1,1]; A064657(n)={n<4 & return(1);

%o #A064657_vec<n & A064657_vec=concat(A064657_vec, vector(n-#A064657_vec)); A064657_vec[n] & return(A064657_vec[n]); A064657_vec[n]=A064657(abs(A064657(n-3)-n))+A064657(abs(A064657(n-4)-n))} \\ - _M. F. Hasler_, Aug 28 2012

%K nonn,fini,full

%O 0,5

%A _Roger L. Bagula_, Oct 08 2001

%E More terms from _Vladeta Jovovic_, Oct 09, 2001

%E Keyword fini added by _Reinhard Zumkeller_, Jul 21 2012