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A033076 Numbers n with property that all pairs of consecutive base 5 digits differ by 3. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)