A192173 - OEIS

%I #21 Jan 24 2025 13:26:06

%S 159,179,189,239,319,389,395,397,399,489,494,498,559,598,629,639,679,

%T 691,695,696,697,698,699,709,789,791,829,839,879,894,895,897,898,917,

%U 935,953,958,962,963,964,965,966,967,968,969,978,981,983,985,986,989

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

%H Robert Israel, <a href="/A192173/b192173.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, May 15 2013

%e (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.

%p filter:= proc(n) local b; `union`(seq(convert(convert(n,base,b),set),b=2..10)) = {$0..9} end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jan 24 2025

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

%o (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

%Y Subsequence of A011539. - _Charles R Greathouse IV_, May 15 2013

%K nonn,base,easy,changed

%O 1,1

%A _Claudio Meller_, Jun 24 2011

%E Corrected by _Harvey P. Dale_, Jul 06 2011