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Search: id:A085509
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| A085509 |
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Numbers containing no zero digits in bases 3 to 10. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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. 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.
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MATHEMATICA
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f[n_] := Count[IntegerDigits[n, {3, 4, 5, 6, 7, 8, 9, 10}], 0, 2]; Select[ Range[351862], f[ # ] == 0 & ]
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CROSSREFS
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Sequence in context: A099419 A061871 A084651 this_sequence A127485 A061385 A156179
Adjacent sequences: A085506 A085507 A085508 this_sequence A085510 A085511 A085512
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 03 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 05 2003
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