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

0, 2, 3, 4, 8, 10, 11, 13, 14, 15, 19, 22, 24, 25, 26, 30, 32, 33, 35, 36, 37, 41, 43, 44, 46, 47, 48, 52, 54, 55, 57, 58, 59, 63, 66, 68, 69, 70, 74, 77, 79, 80, 81, 85, 88, 90, 91, 92, 96, 98, 99, 101, 102, 103, 107, 110, 112, 113, 114, 118, 120, 121, 123, 124, 125, 129

Offset: 1

Author

N. J. A. Sloane, Dec 07 2016

Keywords

• nonn

Comments

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

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

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

Links

• Hao Fu and G.-N. Han, Computer assisted proof for Apwenian sequences related to Hankel determinants, arXiv preprint arXiv:1601.04370 [math.NT], 2016.

Crossrefs

Complement of A279001.

Cf. A279194, A279195.

Programs

Maple

isA279000 := proc(n)
    local x,dgs11,i ;
    x := n+1 ;
    dgs11 := convert(x,base,11) ;
    for i from 1 to nops(dgs11) do
        if op(i,dgs11) in {1,3,4,5,9} then
            return true;
        elif op(i,dgs11) in {2,6,7,8,10} then
            return false;
        end if;
    end do:
    false ;
end proc:
for n from 0 to 200 do
    if isA279000(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 15 2016

Mathematica

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 *)

Python

from sympy import integer_log
def A279000(n):
    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))
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 23 2025

Extensions

Corrected by Lars Blomberg (10 added, 21 removed, 32 added...), Dec 15 2016