A139819 Complement of repdigit numbers A010785.

10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 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

Offset: 1

Author

N. J. A. Sloane, Jun 02 2008

Keywords

• nonn
• base

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Repdigit.
• Wikipedia, Repdigit
• Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024.

Crossrefs

Cf. A066484 (subsequence).

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

Programs

Haskell

a139819 n = a139819_list !! (n-1)
a139819_list = filter ((== 0) . a202022) [0..] -- Reinhard Zumkeller, Dec 09 2011

Maple

isA139819 := proc(n)
    convert(n,base,10) ;
    convert(%,set) ;
    simplify(nops(%) >1 ) ;
end proc: # R. J. Mathar, Jan 17 2017

PARI

is_A139819(n)=#Set(digits(n))>1 \\ M. F. Hasler, Sep 08 2015

Python

def A139819(n):
    m, k = n, n+9*((l:=len(str(n)))-1)+9*n//(10**l-1)
    while m != k:
        m, k = k, n+9*((l:=len(str(k)))-1)+9*k//(10**l-1)
    return m # Chai Wah Wu, Sep 04 2024

Formula

A202022(a(n)) = 0. - Reinhard Zumkeller, Dec 09 2011