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Search: id:A072222
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| A072222 |
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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. |
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+0
1
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| 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, 21, 20, 17, 23, 22, 19, 25, 24, 21, 27, 26, 23, 29, 28, 25, 31, 30, 27, 33, 32, 29, 35, 34, 31, 37, 36, 33, 39, 38, 35, 41, 40, 37, 43, 42, 39, 45, 44, 41, 47, 46, 43, 49, 48, 45, 51
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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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.
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
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REFERENCES
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Published in TFTN as the Bagula Batrachion in 1997.
Clifford A. Pickover, The Crying of Fractal Bactrachion 1,489. Chaos and Graphics, Comput. and Graphics, vol. 19, N0.4, paes 611-615, 1995
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FORMULA
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For n>6, a(n) = a(n-3) + 2 (conjectured). - R. Stephan, May 09 2004
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MATHEMATICA
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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}]
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PROGRAM
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(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
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CROSSREFS
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Sequence in context: A130815 A084129 A011503 this_sequence A005752 A098494 A008955
Adjacent sequences: A072219 A072220 A072221 this_sequence A072223 A072224 A072225
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 04 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 15 2002
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