|
%I #24 Jan 09 2020 03:26:17
%S 1113,1131,1311,2226,2262,2622,3111,3339,3393,3933,6222,9333,11133,
%T 11313,11331,13113,13131,13311,22266,22626,22662,26226,26262,26622,
%U 31113,31131,31311,33111,33399,33939,33993,39339,39393,39933,62226,62262,62622,66222,93339,93393,93933,99333,111333,111339,111393
%N 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.
%C "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).
%C Subsequence of A034838, A052382 and of A139819. - _Reinhard Zumkeller_, Nov 29 2012
%H Reinhard Zumkeller, <a href="/A066484/b066484.txt">Table of n, a(n) for n = 1..1000</a>
%H Ken Duisenberg, Puzzle of the Week (Dec 14, 2001), <a href="http://www.ecst.csuchico.edu/~kend/potw/archive/011214.html">Dividing Rotated Numbers</a>
%e The rotations of 137179 are 371791, 717913, 179137, 791371, 913717, 137179; all these are divisible by 1, 3, 7 and 9.
%t 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 *)
%o (Haskell)
%o -- import Data.List (nub, inits, tails)
%o a066484 n = a066484_list !! (n-1)
%o a066484_list = filter h [1..] where
%o h x = notElem '0' xs && length (nub xs) > 1 &&
%o all d (map read $ zipWith (++)
%o (tail $ tails xs) (tail $ inits xs)) where xs = show x
%o d u = g u where
%o g v = v == 0 || mod u d == 0 && g v' where (v', d) = divMod v 10
%o -- _Reinhard Zumkeller_, Nov 29 2012
%o (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
%K base,nice,nonn
%O 1,1
%A Sudipta Das (juitech(AT)vsnl.net), Jan 02 2002
%E Corrected and extended by _Harvey P. Dale_, Mar 30 2011
%E Definition reworded by _M. F. Hasler_, Jan 05 2020
|
