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A066484
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Numbers with at least 2 distinct digits and whose "rotations" (including the number itself) are multiples of these digits; repeated digits allowed but digit 0 not allowed.
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5
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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;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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"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 gives back the original number).
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LINKS
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EXAMPLE
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The rotations of 137179 are 371791, 717913, 179137, 791371, 913717, 137179; all these are divisible by 1, 3, 7 and 9.
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MATHEMATICA
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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] (* Harvey P. Dale, Mar 30 2011 *)
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PROG
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(Haskell)
-- import Data.List (nub, inits, tails)
a066484 n = a066484_list !! (n-1)
a066484_list = filter h [1..] where
h x = notElem '0' xs && length (nub xs) > 1 &&
all d (map read $ zipWith (++)
(tail $ tails xs) (tail $ inits xs)) where xs = show x
d u = g u where
g v = v == 0 || mod u d == 0 && g v' where (v', d) = divMod v 10
(PARI) select( {is_A066484(n, d=Set(digits(n)))= d[1] && #d>1 && (d[1]>1||d=d[^1]) && !for(i=0, logint(n, 10), n=[1, 10^logint(n, 10)]*divrem(n, 10); [n%x|x<-d]&&return)}, [1..10^5]) \\ M. F. Hasler, Jan 05 2020
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CROSSREFS
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KEYWORD
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base,nice,nonn
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AUTHOR
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Sudipta Das (juitech(AT)vsnl.net), Jan 02 2002
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EXTENSIONS
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STATUS
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approved
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