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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

%I #18 Aug 05 2017 05:46:11

%S 3,19,118,709,4259,25557,153343,920062,5520373,33122243,198733461,

%T 1192400767,7154404606,42926427637,257558565827,1545351394965,

%U 9272108369791,55632650218750,333795901312501,2002775407875011,12016652447250069,72099914683500415

%N 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).

%H Colin Barker, <a href="/A290477/b290477.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,0,0,1,-6).

%F From _Colin Barker_, Aug 04 2017: (Start)

%F 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)).

%F a(n) = 6*a(n-1) + a(n-5) - 6*a(n-6) for n>6.

%F (End)

%e Base 6...........Decimal

%e 3......................3

%e 31....................19

%e 314..................118

%e 3141.................709

%e 31415...............4259

%e 314153.............25557

%e 3141531...........153343

%e etc. - _Colin Barker_, Aug 04 2017

%t 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]

%o (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

%K nonn,base,easy

%O 1,1

%A _Harvey P. Dale_, Aug 03 2017

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)