login
A280824
Numbers with an even number of digits and with an even number of distinct digits.
4
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
1,1
COMMENTS
Differs from A139819 (the latter contains 100, for example). - R. J. Mathar, Jan 17 2017
LINKS
Eric Weisstein's World of Mathematics, Digit
FORMULA
A000035(A055642(a(n))) = 0.
A000035(A043537(a(n))) = 0.
a(n) = A029742(n) for n < 82.
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 & ]
PROG
(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
KEYWORD
nonn,base,easy
AUTHOR
Ilya Gutkovskiy, Jan 08 2017
STATUS
approved