A279001 Numbers of the form (11*h+j)*11^k-1 for h,k in N and j in {2,6,7,8,10}.

1, 5, 6, 7, 9, 12, 16, 17, 18, 20, 21, 23, 27, 28, 29, 31, 34, 38, 39, 40, 42, 45, 49, 50, 51, 53, 56, 60, 61, 62, 64, 65, 67, 71, 72, 73, 75, 76, 78, 82, 83, 84, 86, 87, 89, 93, 94, 95, 97, 100, 104, 105, 106, 108, 109, 111, 115, 116, 117, 119, 122, 126, 127

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

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 A279000.

Cf. A279194, A279195.

Programs

Maple

isA279001 := proc(n)
    not isA279000(n) ;
end proc:
for n from 0 to 200 do
    if isA279001(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 15 2016

Mathematica

okQ[n_] := Not @ MatchQ[IntegerDigits[n+1, 11], {_, 1|3|4|5|9, 0...}];
Select[Range[200], okQ] (* Jean-François Alcover, Feb 25 2018, after R. J. Mathar *)

Python

from sympy import integer_log
def A279001(n):
    def f(x): return n-1+sum(((m:=(x+1)//11**i)-1)//11+(m-3)//11+(m-4)//11+(m-5)//11+(m-9)//11+5 for i in range(integer_log(x+1,11)[0]+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 23 2025

Extensions

Corrected by Lars Blomberg (base 5 replaced by base 11. 10 removed, 21 added,...), Dec 15 2016