A085509 - OEIS

%I #11 Oct 16 2021 16:02:31

%S 1,2,13,22,23,43,121,122,157,158,214,619,5471,5557,5561,5791,5818,

%T 5819,5821,5822,38299,38357,38362,38363,38366,58711,58714,58966,58967,

%U 154213,154214,154219,154222,154223,154534,154537,154538,154543,154997,351742

%N Numbers containing no zero digits in bases 3 to 10.

%C To extend to base 2 only numbers of the form 2^n-1 need to be considered, since all others have zero digits in base 2.

%C Tested up to 2^45 - 1 and found no term (other than 1) which doesn't contain zeros in one of the other bases 3 to 10.

%C Tested up to 2^50000 - 1 and found no such term. - _Robert G. Wilson v_

%C Several of these come in pairs such as 1 & 2, 22 & 23, 121 & 122, 157 & 158, 5818 & 5819, etc. See A085828. There is also a near-triple in 154534, 154537, 154538, 154543.

%C But no such triple can exist, since, given three consecutive numbers, one must be divisible by 3, which implies that it ends in a zero in base 3. - _Robert G. Wilson v_

%H Chai Wah Wu, <a href="/A085509/b085509.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_] := Count[IntegerDigits[n, {3, 4, 5, 6, 7, 8, 9, 10}], 0, 2]; Select[ Range[351862], f[ # ] == 0 & ]

%t Select[Range[352000],FreeQ[Flatten[IntegerDigits[#,Range[3,10]]],0]&] (* _Harvey P. Dale_, Oct 16 2021 *)

%K base,nonn

%O 1,2

%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 03 2003

%E Edited and extended by _Robert G. Wilson v_, Jul 05 2003