A052191 Smallest multiple of n with no isolated digits.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 11, 444, 1144, 3388, 555, 2288, 1122, 666, 2299, 1100, 777, 22, 2277, 888, 1100, 1144, 999, 3388, 2233, 3300, 4433, 6688, 33, 1122, 1155, 1188, 111, 3344, 5577, 2200, 2255, 5544, 3311, 44, 4455, 5566, 7755

Offset

1,1

Comments

a(n) = n * A052192(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

a(23)=2277 since 23*99=2277 and all the digits of 2277 have a neighboring digit which is the same.

Mathematica

isol[n_ ] := Module[{}, L={11}~Join~IntegerDigits[n ]~Join~{11}; l=Length[L ]; Apply[And, Table[L[[i ] ]==L[[i-1 ] ]||L[[i ] ]==L[[i+1 ] ], {i, 2, l-1} ] ] ] a[n_ ] := a[n ]=Module[{}, m=0; While[Not[isol[m ] ], m=m+n ]; m ] Table[a[i ], {i, 1, 100} ]
smn[n_]:=Module[{k=1}, While[Min[Length/@Split[IntegerDigits[k*n]]]<2, k++]; k*n]; Array[smn, 50] (* Harvey P. Dale, Oct 19 2018 *)

Prog

(Haskell)
import Data.List (group)
a052191 n = head $
   filter ((> 1) . minimum . map length . group . show) $ [0, n..]
-- Reinhard Zumkeller, Sep 15 2011
(Python)
def A052191(n):
    k = 0
    while True:
        k += n
        x = split('(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)', str(k))
        for d in x:
            if len(d) == 1:
                break
        else:
            return k # Chai Wah Wu, Jan 03 2015

Crossrefs

Sequence in context: A110745 A280826 A020338 * A321536 A110732 A044836

Adjacent sequences: A052188 A052189 A052190 * A052192 A052193 A052194

Keyword

base,easy,nice,nonn,look

Author

Erich Friedman, Jan 28 2000

Status

approved