A033076 Numbers in which all pairs of consecutive base-5 digits differ by 3.

1, 2, 3, 4, 9, 15, 21, 46, 78, 109, 234, 390, 546, 1171, 1953, 2734, 5859, 9765, 13671, 29296, 48828, 68359, 146484, 244140, 341796, 732421, 1220703, 1708984, 3662109, 6103515, 8544921, 18310546, 30517578, 42724609, 91552734, 152587890, 213623046, 457763671

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..3860

Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,1,0,0,-5).

Formula

G.f.: x*(5*x^10+5*x^9-x^7-x^4-x^3+3*x^2+2*x+1) / (5*x^9-x^6-5*x^3+1). - Colin Barker, May 31 2015

a(n) = 5*a(n-3)+a(n-6)-5*a(n-9) for n>11. - Colin Barker, Jun 01 2015

For k >=1, a(3*k+1) = (7*5^k-2*(-1)^k-5)/8, a(3*k+2) = (15*5^k-2*(-1)^k-5)/8 and a(3*k+3) = (5^(k+2)+ 2*(-1)^k-3)/8. - Robert Israel, Jun 01 2015

Maple

1, 2, 3, seq(op([(7*5^k-2*(-1)^k-5)/8, (15*5^k-2*(-1)^k-5)/8, (5^(k+2)+ 2*(-1)^k-3)/8]), k=1..20); # Robert Israel, Jun 01 2015

Mathematica

Join[{1, 2, 3, 4}, Select[Range[5000000], Union[Abs[Differences[ IntegerDigits[ #, 5]]]]=={3}&]] (* Harvey P. Dale, Apr 17 2013 *)

Prog

(PARI) Vec(x*(5*x^10+5*x^9-x^7-x^4-x^3+3*x^2+2*x+1)/(5*x^9-x^6-5*x^3+1) + O(x^100)) \\ Colin Barker, Jun 01 2015

Crossrefs

Sequence in context: A122974 A032982 A288856 * A121431 A084080 A124753

Adjacent sequences: A033073 A033074 A033075 * A033077 A033078 A033079

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, Apr 17 2013

More terms from Robert Israel, Jun 01 2015

Status

approved