A052192 Smallest a(n) for which n*a(n) has no isolated digits.

11, 11, 11, 11, 11, 11, 11, 11, 11, 110, 1, 37, 88, 242, 37, 143, 66, 37, 121, 55, 37, 1, 99, 37, 44, 44, 37, 121, 77, 110, 143, 209, 1, 33, 33, 33, 3, 88, 143, 55, 55, 132, 77, 1, 99, 121, 165, 706, 678, 22, 22, 22, 22, 22, 1, 99, 1169, 77, 132, 55, 55, 143, 88, 121

Offset

1,1

Comments

a(n) = A052191(n) / n.

Links

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

Example

a(23)=99 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} ]/Range[100 ]
nid[n_]:=Module[{k=1}, While[Min[Length/@Split[IntegerDigits[k n]]]<2, k++]; k]; Array[nid, 70] (* Harvey P. Dale, Nov 04 2024 *)

Prog

(Haskell)
import Data.List (group, findIndex)
import Data.Maybe (fromJust)
a052192 n = fromJust $
   findIndex ((> 1) . minimum . map length . group . show) $ [0, n..]
-- Reinhard Zumkeller, Sep 15 2011

Crossrefs

Sequence in context: A113587 A083971 A240453 * A110733 A090862 A291498

Adjacent sequences: A052189 A052190 A052191 * A052193 A052194 A052195

Keyword

base,easy,nice,nonn,look

Author

Erich Friedman, Jan 28 2000

Status

approved