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A006288
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Loxton-van der Poorten sequence: base-4 representation contains only -1, 0, +1.
(Formerly M2312)
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4
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0, 1, 3, 4, 5, 11, 12, 13, 15, 16, 17, 19, 20, 21, 43, 44, 45, 47, 48, 49, 51, 52, 53, 59, 60, 61, 63, 64, 65, 67, 68, 69, 75, 76, 77, 79, 80, 81, 83, 84, 85, 171, 172, 173, 175, 176, 177, 179, 180, 181, 187, 188, 189, 191, 192, 193, 195, 196, 197, 203, 204, 205, 207, 208, 209
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Recurrence: a(3n) = 4a(n), a(3n-1) = 4a(n)-1, a(3n+1) = 4a(n)+1, starting 0,1. - Ralf Stephan, Jan 19 2014
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EXAMPLE
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1*4^2 + 0*4^1 + (-1)*4^0 = 15, so 15 is in sequence.
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PROG
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(PARI) a(n)=if(n<2, n>0, 4*a((n+1)\3)+(n+1)%3-1) \\ Ralf Stephan, Jan 19 2014
(PARI) a(n) = my(v=digits(n, 3), prev=0); forstep(i=#v, 1, -1, prev=(v[i]+=(v[i]>(prev<2)))); fromdigits(v, 4); \\ Kevin Ryde, Jun 03 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Offset changed to 0 and example added by Ralf Stephan, Jan 19 2014
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STATUS
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approved
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