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A290477
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).
1
3, 19, 118, 709, 4259, 25557, 153343, 920062, 5520373, 33122243, 198733461, 1192400767, 7154404606, 42926427637, 257558565827, 1545351394965, 9272108369791, 55632650218750, 333795901312501, 2002775407875011, 12016652447250069, 72099914683500415
OFFSET
1,1
FORMULA
From Colin Barker, Aug 04 2017: (Start)
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)
EXAMPLE
Base 6...........Decimal
3......................3
31....................19
314..................118
3141.................709
31415...............4259
314153.............25557
3141531...........153343
etc. - Colin Barker, Aug 04 2017
MATHEMATICA
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]
PROG
(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
CROSSREFS
Sequence in context: A084133 A005667 A098444 * A321002 A221184 A274852
KEYWORD
nonn,base,easy
AUTHOR
Harvey P. Dale, Aug 03 2017
STATUS
approved