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A290477
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Base 6 digits are, in order, the first n terms of the periodic sequence with initial period 3,1,4,1,5 (the first five digits of Pi).
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1
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3, 19, 118, 709, 4259, 25557, 153343, 920062, 5520373, 33122243, 198733461, 1192400767, 7154404606, 42926427637, 257558565827, 1545351394965, 9272108369791, 55632650218750, 333795901312501, 2002775407875011, 12016652447250069, 72099914683500415
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: x*(3 + x + 4*x^2 + x^3 + 5*x^4) / ((1 - x)*(1 - 6*x)*(1 + x + x^2 + x^3 + x^4)).
a(n) = 6*a(n-1) + a(n-5) - 6*a(n-6) for n>6.
(End)
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EXAMPLE
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Base 6...........Decimal
3......................3
31....................19
314..................118
3141.................709
31415...............4259
314153.............25557
3141531...........153343
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MATHEMATICA
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Table[FromDigits[PadRight[{}, n, {3, 1, 4, 1, 5}], 6], {n, 30}] (* or *) LinearRecurrence[{6, 0, 0, 0, 1, -6}, {3, 19, 118, 709, 4259, 25557}, 30]
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PROG
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(PARI) Vec(x*(3 + x + 4*x^2 + x^3 + 5*x^4) / ((1 - x)*(1 - 6*x)*(1 + x + x^2 + x^3 + x^4)) + O(x^30)) \\ Colin Barker, Aug 04 2017
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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