A033077 Numbers in which all pairs of consecutive base-6 digits differ by 3.

1, 2, 3, 4, 5, 10, 17, 18, 25, 32, 61, 104, 111, 154, 197, 370, 629, 666, 925, 1184, 2221, 3776, 3999, 5554, 7109, 13330, 22661, 23994, 33325, 42656, 79981, 135968, 143967, 199954, 255941, 479890, 815813, 863802, 1199725, 1535648, 2879341, 4894880, 5182815

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+4*x^5+5*x^6+1*x^8+2*x^9)*x / (1-6*x^5-1*x^10+6*x^15). - Alois P. Heinz, Feb 25 2011

a(n) = 6*a(n-5)+a(n-10)-6*a(n-15) for n>15. - Colin Barker, Jun 01 2015

Maple

a:= proc(n) local c, d, i, m; c, d:= 0, 1+irem(n-1, 5, 'm'); for i to m+1 do c:= 6*c +d; d:= d +`if`(d<3, 3, -3) od; c end:
seq(a(n), n=1..50);  # Alois P. Heinz, Feb 26 2011

Mathematica

Join[Range[5], Select[Range[52*10^5], Union[Abs[Differences[ IntegerDigits[ #, 6]]]] == {3}&]] (* Harvey P. Dale, Oct 25 2020 *)

Prog

(PARI) Vec((1+2*x+3*x^2+4*x^3+5*x^4+4*x^5+5*x^6+1*x^8+2*x^9)*x/ (1-6*x^5-1*x^10+6*x^15) + O(x^100)) \\ Colin Barker, Jun 01 2015

Crossrefs

Cf. A033082.

Sequence in context: A179146 A099161 A369592 * A190912 A306108 A282033

Adjacent sequences: A033074 A033075 A033076 * A033078 A033079 A033080

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved