A085509 Numbers containing no zero digits in bases 3 to 10.

1, 2, 13, 22, 23, 43, 121, 122, 157, 158, 214, 619, 5471, 5557, 5561, 5791, 5818, 5819, 5821, 5822, 38299, 38357, 38362, 38363, 38366, 58711, 58714, 58966, 58967, 154213, 154214, 154219, 154222, 154223, 154534, 154537, 154538, 154543, 154997, 351742

Offset

1,2

Comments

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.

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.

Tested up to 2^50000 - 1 and found no such term. - Robert G. Wilson v

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.

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

f[n_] := Count[IntegerDigits[n, {3, 4, 5, 6, 7, 8, 9, 10}], 0, 2]; Select[ Range[351862], f[ # ] == 0 & ]
Select[Range[352000], FreeQ[Flatten[IntegerDigits[#, Range[3, 10]]], 0]&] (* Harvey P. Dale, Oct 16 2021 *)

Crossrefs

Sequence in context: A303669 A084651 A285087 * A127485 A061385 A366208

Adjacent sequences: A085506 A085507 A085508 * A085510 A085511 A085512

Keyword

base,nonn

Author

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

Extensions

Edited and extended by Robert G. Wilson v, Jul 05 2003

Status

approved