A139819 - OEIS

%I #31 Sep 17 2024 10:36:24

%S 10,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,34,35,

%T 36,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,54,56,57,58,59,60,

%U 61,62,63,64,65,67,68,69,70,71,72,73,74,75,76,78,79,80,81,82,83,84,85,86,87,89

%N Complement of repdigit numbers A010785.

%C Identical to (base 10) non-palindromic numbers A029742 up to a(83) = 101 which is a term of this sequence but not in A029742. - _M. F. Hasler_, Sep 08 2015

%H Reinhard Zumkeller, <a href="/A139819/b139819.txt">Table of n, a(n) for n = 1..10000</a>

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Repdigit">Repdigit</a>

%H Chai Wah Wu, <a href="https://arxiv.org/abs/2409.05844">Algorithms for complementary sequences</a>, arXiv:2409.05844 [math.NT], 2024.

%F A202022(a(n)) = 0. - _Reinhard Zumkeller_, Dec 09 2011

%p isA139819 := proc(n)

%p     convert(n,base,10) ;

%p     convert(%,set) ;

%p     simplify(nops(%) >1 ) ;

%p end proc: # _R. J. Mathar_, Jan 17 2017

%o (Haskell) a139819 n = a139819_list !! (n-1)

%o a139819_list = filter ((== 0) . a202022) [0..] -- _Reinhard Zumkeller_, Dec 09 2011

%o (PARI) is_A139819(n)=#Set(digits(n))>1 \\ _M. F. Hasler_, Sep 08 2015

%o (Python)

%o def A139819(n):

%o     m, k = n, n+9*((l:=len(str(n)))-1)+9*n//(10**l-1)

%o     while m != k:

%o         m, k = k, n+9*((l:=len(str(k)))-1)+9*k//(10**l-1)

%o     return m # _Chai Wah Wu_, Sep 04 2024

%Y Cf. A066484 (subsequence).

%Y Cf. A029742 (non-palindromic in base 10), A016038 (in any base), A050813 (in bases 2..10).

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Jun 02 2008