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A048333 Numbers that are repdigits in base 8. 5
0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 73, 146, 219, 292, 365, 438, 511, 585, 1170, 1755, 2340, 2925, 3510, 4095, 4681, 9362, 14043, 18724, 23405, 28086, 32767, 37449, 74898, 112347, 149796, 187245, 224694, 262143, 299593, 599186, 898779 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For the general case, the sequence of numbers that are repdigits in base b > 1 satisfies the recurrence a(n) = (b+1)*a(n-b+1) - b*a(n-2*(b-1)) for n >= 2(b-1) with g.f.: (sum_{1 <= i < b} i*x^i)/(1 - (b+1)*x^(b-1) + bx^(2(b-1))). - Chai Wah Wu, May 30 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Eric Weisstein's World of Mathematics, Repdigit

Index entries for 2-automatic sequences.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, -8).

FORMULA

From Chai Wah Wu, May 30 2016: (Start)

a(n) = 9*a(n-7) - 8*a(n-14) for n > 13.

G.f.: x*(7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(8*x^14 - 9*x^7 + 1). (End)

MATHEMATICA

Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 8], {n, 0, 40}, {d, 7}]]] (* Vincenzo Librandi, Feb 06 2014 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, -8}, {0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54}, 50] (* Harvey P. Dale, Dec 09 2018 *)

PROG

(PARI) is(n)=#Set(digits(n, 8))==1 \\ Charles R Greathouse IV, Feb 15 2017

CROSSREFS

Cf. A010785, A033021, A028987, A028988.

Sequence in context: A297265 A048319 A037405 * A007496 A082274 A029804

Adjacent sequences:  A048330 A048331 A048332 * A048334 A048335 A048336

KEYWORD

nonn,base,easy

AUTHOR

Patrick De Geest, Feb 15 1999

EXTENSIONS

Changed offset from 1 to 0 by Vincenzo Librandi, Feb 06 2014

STATUS

approved

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Last modified January 27 09:09 EST 2020. Contains 331293 sequences. (Running on oeis4.)