Search: id:A072222
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%I A072222
%S A072222 1,1,0,1,5,4,1,7,6,3,9,8,5,11,10,7,13,12,9,15,14,11,17,16,13,19,18,15,
%T A072222 21,20,17,23,22,19,25,24,21,27,26,23,29,28,25,31,30,27,33,32,29,35,34,
%U A072222 31,37,36,33,39,38,35,41,40,37,43,42,39,45,44,41,47,46,43,49,48,45,51
%N A072222 a(n) = mod(abs(n-1-a(n-2)],n) + mod(abs(n-1-a(n-1)],n-1], a(0) = 1, a(1) 
               = 1.
%C A072222 A Batrachian-like sequence inspired by Clifford Pickover's article. It 
               uses a combination of a modulus and absolute value to keep the index 
               in range.
%C A072222 Proof of conjecture: If a(n) is in a suitable range, it is possible to 
               omit the abs and the mod function. So for n>6, a(n) simplifies to 
               a(n) = 2n-2 - a(n-1) - a(n-2). Substituting a(n-1), we get a(n)=2n-2 
               - (2(n-1)-2 -a(n-2) - a(n-3)) - a(n-2) = a(n-3) + 2, as conjectured. 
               - Lambert Herrgesell (zero815(AT)googlemail.com), Jan 18 2007
%D A072222 Published in TFTN as the Bagula Batrachion in 1997.
%D A072222 Clifford A. Pickover, The Crying of Fractal Bactrachion 1,489. Chaos 
               and Graphics, Comput. and Graphics, vol. 19, N0.4, paes 611-615, 
               1995
%F A072222 For n>6, a(n) = a(n-3) + 2 (conjectured). - R. Stephan, May 09 2004
%t A072222 f[n_] := f[n] = Mod[ Abs[n - 1 - f[n - 2]], n] + Mod[ Abs[n - 1 - f[n 
               - 1]], n - 1]; f[0] = 1; f[1] = 1; Table[ f[n], {n, 0, 75}]
%o A072222 (TRUE BASIC) DIM f(0 to 640) SET MODE "color" SET WINDOW 0,640,0,480 
               SET COLOR MIX (1) 0,0,0 LET f(0)=1 LET f(1)=1 REM Bagula Batrachion 
               PRINT"BAGULA BATRACHION:" FOR k= 2 to 75 LET g=mod(abs(k-1-f(k-2)),
               k) LET h=mod(abs(k-1-f(k-1)),k-1) LET f(k)=g+h SET COLOR 1 IF F(K)<>
               0 THEN PLOT K,240+120*F(K-1)/F(K) SET COLOR 255 PRINT K,F(K) NEXT 
               k END
%Y A072222 Sequence in context: A130815 A084129 A011503 this_sequence A005752 A098494 
               A008955
%Y A072222 Adjacent sequences: A072219 A072220 A072221 this_sequence A072223 A072224 
               A072225
%K A072222 nonn
%O A072222 0,5
%A A072222 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 04 2002
%E A072222 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 15 2002

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