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).

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,0,0,0,1,-6).

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

Adjacent sequences: A290474 A290475 A290476 * A290478 A290479 A290480

Keyword

nonn,base,easy

Author

Harvey P. Dale, Aug 03 2017

Status

approved