login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048333 Numbers that are repdigits in base 8. 5

%I #33 Jan 21 2022 05:08:08

%S 0,1,2,3,4,5,6,7,9,18,27,36,45,54,63,73,146,219,292,365,438,511,585,

%T 1170,1755,2340,2925,3510,4095,4681,9362,14043,18724,23405,28086,

%U 32767,37449,74898,112347,149796,187245,224694,262143,299593,599186,898779

%N Numbers that are repdigits in base 8.

%C 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

%H Vincenzo Librandi, <a href="/A048333/b048333.txt">Table of n, a(n) for n = 0..700</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repdigit.html">Repdigit</a>.

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,9,0,0,0,0,0,0,-8).

%F From _Chai Wah Wu_, May 30 2016: (Start)

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

%F 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)

%F Sum_{n>=1} 1/a(n) = (363/20) * A248725 = 2.92153624531838250201... - _Amiram Eldar_, Jan 21 2022

%t Union[Flatten[Table[FromDigits[PadRight[{}, n, d], 8], {n, 0, 40}, {d, 7}]]] (* _Vincenzo Librandi_, Feb 06 2014 *)

%t 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 *)

%o (PARI) is(n)=#Set(digits(n,8))==1 \\ _Charles R Greathouse IV_, Feb 15 2017

%Y Cf. A010785, A033021, A028987, A028988, A248725.

%K nonn,base,easy

%O 0,3

%A _Patrick De Geest_, Feb 15 1999

%E Changed offset from 1 to 0 by _Vincenzo Librandi_, Feb 06 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)