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A279000 Numbers of the form (11*h+j)*11^k-1 for h,k in N and j in {1,3,4,5,9}.

%I A279000 #39 Feb 23 2025 01:43:44
%S A279000 0,2,3,4,8,10,11,13,14,15,19,22,24,25,26,30,32,33,35,36,37,41,43,44,
%T A279000 46,47,48,52,54,55,57,58,59,63,66,68,69,70,74,77,79,80,81,85,88,90,91,
%U A279000 92,96,98,99,101,102,103,107,110,112,113,114,118,120,121,123,124,125,129
%N A279000 Numbers of the form (11*h+j)*11^k-1 for h,k in N and j in {1,3,4,5,9}.
%C A279000 Created in a failed attempt to explain sequences J and K on page 10 of Fu and Han (2016). See A279194 and A279195. - _N. J. A. Sloane_, Dec 15 2016
%C A279000 Numbers n such that the least-significant non-0 digit of n+1 in base 11 is one of {1,3,4,5,9}. - _R. J. Mathar_, Dec 15 2016
%C A279000 It appears that the correct J and K have form more closely resembling the J and K of F_3(n): n is in J if either k is odd and j is in {2,6,7,8,10} or k is even and j is in {1,3,4,5,9}, and n is in K if either k is even and j is in {2,6,7,8,10} or k is odd and j is in {1,3,4,5,9}. - _Charlie Neder_, Mar 10 2019
%H A279000 Hao Fu and G.-N. Han, <a href="https://arxiv.org/abs/1601.04370">Computer assisted proof for Apwenian sequences related to Hankel determinants</a>, arXiv preprint arXiv:1601.04370 [math.NT], 2016.
%p A279000 isA279000 := proc(n)
%p A279000     local x,dgs11,i ;
%p A279000     x := n+1 ;
%p A279000     dgs11 := convert(x,base,11) ;
%p A279000     for i from 1 to nops(dgs11) do
%p A279000         if op(i,dgs11) in {1,3,4,5,9} then
%p A279000             return true;
%p A279000         elif op(i,dgs11) in {2,6,7,8,10} then
%p A279000             return false;
%p A279000         end if;
%p A279000     end do:
%p A279000     false ;
%p A279000 end proc:
%p A279000 for n from 0 to 200 do
%p A279000     if isA279000(n) then
%p A279000         printf("%d,",n) ;
%p A279000     end if;
%p A279000 end do: # _R. J. Mathar_, Dec 15 2016
%t A279000 okQ[n_] := MatchQ[IntegerDigits[n+1, 11], {___, 1 | 3 | 4 | 5 | 9, 0...}]; Select[Range[0, 200], okQ] (* _Jean-François Alcover_, Feb 25 2018, after _R. J. Mathar_ *)
%o A279000 (Python)
%o A279000 from sympy import integer_log
%o A279000 def A279000(n):
%o A279000     def f(x): return n-1+sum(((m:=(x+1)//11**i)-2)//11+(m-6)//11+(m-7)//11+(m-8)//11+(m-10)//11+5 for i in range(integer_log(x+1,11)[0]+1))
%o A279000     m, k = n-1, f(n-1)
%o A279000     while m != k: m, k = k, f(k)
%o A279000     return m # _Chai Wah Wu_, Feb 23 2025
%Y A279000 Complement of A279001.
%Y A279000 Cf. A279194, A279195.
%K A279000 nonn
%O A279000 1,2
%A A279000 _N. J. A. Sloane_, Dec 07 2016
%E A279000 Corrected by _Lars Blomberg_ (10 added, 21 removed, 32 added...), Dec 15 2016