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A052191 Smallest multiple of n with no isolated digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)