A066484 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.

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

Offset

1,1

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 gives back the original number).

Subsequence of A034838, A052382 and of A139819. - Reinhard Zumkeller, Nov 29 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Ken Duisenberg, Puzzle of the Week (Dec 14, 2001), Dividing Rotated Numbers

Example

The rotations of 137179 are 371791, 717913, 179137, 791371, 913717, 137179; all these are divisible by 1, 3, 7 and 9.

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]  (* Harvey P. Dale, Mar 30 2011 *)

Prog

(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
-- Reinhard Zumkeller, Nov 29 2012
(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

Crossrefs

Sequence in context: A236050 A213979 A225351 * A199982 A151951 A190017

Adjacent sequences: A066481 A066482 A066483 * A066485 A066486 A066487

Keyword

base,nice,nonn

Author

Sudipta Das (juitech(AT)vsnl.net), Jan 02 2002

Extensions

Corrected and extended by Harvey P. Dale, Mar 30 2011

Definition reworded by M. F. Hasler, Jan 05 2020

Status

approved