A280824 Numbers with an even number of digits and with an even number of distinct digits.

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, 90, 91, 92, 93, 94, 95, 96, 97, 98, 1000, 1001, 1010

Offset: 1

Author

Ilya Gutkovskiy, Jan 08 2017

Keywords

• nonn
• base
• easy

Comments

Differs from A139819 (the latter contains 100, for example). - R. J. Mathar, Jan 17 2017

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digit
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A000035, A001637, A029742, A043537, A055642, A280823, A280825, A280826.

Programs

Maple

isA280824 := proc(n)
    if n < 10 then
        return false;
    end if;
    dgs := convert(n,base,10) ;
    if type(nops(dgs),'even') then
        type(nops(convert(dgs,set)),'even') ;
    else
        false;
    end if;
end proc: # R. J. Mathar, Jan 17 2017

Mathematica

Select[Range[1010], Mod[Length[IntegerDigits[#1]], 2] == 0 && Mod[Length[Union[IntegerDigits[#1]]], 2] == 0 & ]

Python

def ok(n): s = str(n); return len(s)%2 == 0 == len(set(s))%2
print(list(filter(ok, range(1011)))) # Michael S. Branicky, Oct 12 2021

Formula

A000035(A055642(a(n))) = 0.

A000035(A043537(a(n))) = 0.

a(n) = A029742(n) for n < 82.