login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
COMMENTS
a(n) = n * A052192(n).
LINKS
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
KEYWORD
base,easy,nice,nonn,look
AUTHOR
Erich Friedman, Jan 28 2000
STATUS
approved