A192173 Numbers whose writing in every base from 2 to 10 requires all ten (0-9) digits at least once.

159, 179, 189, 239, 319, 389, 395, 397, 399, 489, 494, 498, 559, 598, 629, 639, 679, 691, 695, 696, 697, 698, 699, 709, 789, 791, 829, 839, 879, 894, 895, 897, 898, 917, 935, 953, 958, 962, 963, 964, 965, 966, 967, 968, 969, 978, 981, 983, 985, 986, 989

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n. - Charles R Greathouse IV, May 15 2013

Example

(159)10 =  (10011111)2 = (12220)3 =(2133)4 = (1114)5 =(423)6=(315)7=(237)8=(186)9 . All digits 0,1,2,3,4,5,7,8,6,9 are used at least once.

Maple

filter:= proc(n) local b; `union`(seq(convert(convert(n, base, b), set), b=2..10)) = {$0..9} end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 24 2025

Mathematica

With[{c=Range[0, 9]}, Select[Range[3000], Union[Flatten[Table[IntegerDigits[#, n], {n, 2, 10}]]]==c&]] (* Harvey P. Dale, Jul 06 2011 *)

Prog

(PARI) isok(k) = my(s=Set()); for (b=2, 10, s = setunion(s, Set(digits(k, b)))); s == Set([0..9]); \\ Michel Marcus, Jan 24 2025

Crossrefs

Subsequence of A011539. - Charles R Greathouse IV, May 15 2013

Sequence in context: A207146 A045260 A280967 * A093472 A270304 A281665

Adjacent sequences: A192170 A192171 A192172 * A192174 A192175 A192176

Keyword

nonn,base,easy,changed

Author

Claudio Meller, Jun 24 2011

Extensions

Corrected by Harvey P. Dale, Jul 06 2011

Status

approved