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A066484
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Consists of at least 2 distinct digits (repetition of digits allowed but zeroes not allowed), all of whose "rotations" (including the number itself) are exact multiples of its distinct digits.
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0
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1113, 1131, 1311, 2226, 2262, 2622, 3111, 3339, 3393, 3933, 6222, 9333, 11133, 11313, 11331, 13113, 13131, 13311, 22266, 22626, 22662, 26226, 26262, 26622, 31113, 31131, 31311, 33111, 33399, 33939, 33993, 39339, 39393, 39933, 62226, 62262, 62622, 66222, 93339, 93393, 93933, 99333, 111333, 111339, 111393
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "Rotation" of a (multi-digit) number involves taking the first digit of the number and putting it at the end to form a new number. For example, successive rotations of 1234 yield the numbers 2341, 3412 and 4123 (Another rotation would give you back the original number).
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LINKS
| Ken Duisenberg, Puzzle of the Week (Dec14,2001), Dividing Rotated Numbers
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EXAMPLE
| The rotations of 137179 are 371791,717913,179137,791371,913717,137179; all these are divisible by 1,3,7,9.
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MATHEMATICA
| ddQ[n_]:=Module[{idn=IntegerDigits[n]}, DigitCount[n, 10, 0]==0 && Length[Union[idn]]>1 && And@@Flatten[Divisible[#, Union[idn]]&/@ (FromDigits/@Table[RotateRight[idn, i], {i, Length[idn]}])]]; Select[Range[10, 200000], ddQ] (* From Harvey P. Dale, Mar 30 2011 *)
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CROSSREFS
| Sequence in context: A015292 A154805 A203897 * A199982 A151951 A190017
Adjacent sequences: A066481 A066482 A066483 * A066485 A066486 A066487
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KEYWORD
| base,nice,nonn
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AUTHOR
| Sudipta Das (juitech(AT)vsnl.net), Jan 02 2002
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, Mar 30 2011.
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