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A232185 Let x(0)x(1)x(2)...x(q) denote the decimal expansion of n. Sequence lists the numbers n > 10 such that x(0)/x(1)x(2)... x(q) + x(0)x(1)/x(2)x(3)...x(q) + ... + x(0)x(1)... x(q-1)/x(q) is an integer where the digits x(i) > 0 for i = 0,1,..q 0
11, 21, 22, 31, 33, 41, 42, 44, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 612, 816, 945 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A232184. This sequence is probably finite (no further terms less than 2*10^8).

The corresponding integers are 1, 2, 1, 3, 1, 4, 2, 1, 5, 1, 6, 3, 2, 1, 7, 1, 8, 4, 2, 1, 9, 3, 1, 31, 14, 19.

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

945 is in the sequence because 9/45  + 94/5 = 19 is integer.

MAPLE

with(numtheory):U:=array(1..10):V:=array(1..10):for n from 1 to 20000 do: x:=convert(n, base, 10):n1:=nops(x): s:=product('x[i]', 'i'=1..n1):if s<>0 then s1:=0:s2:=0:for i from 1 to n1 do:s1:=s1+x[i]*10^(i-1): U[i]:=s1:od: s2:=x[n1]:V[n1]:=s2:for j from n1-1 by -1 to 1 do:s2:=s2*10+x[j]:V[j]:=s2:od:s3:=0:ii:=0:for k from n1 by -1 to 2 while(ii=0) do:if U[k-1]=0 then ii:=1: else s3:=s3+V[k]/U[k-1]:fi:od:if s3=floor(s3) and ii=0 then printf(`%d, `, n):else fi:fi:od:

CROSSREFS

Cf. A084906, A232184.

Sequence in context: A108237 A084906 A232184 * A118853 A117841 A105956

Adjacent sequences:  A232182 A232183 A232184 * A232186 A232187 A232188

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Nov 20 2013

STATUS

approved

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Last modified April 17 01:55 EDT 2021. Contains 343054 sequences. (Running on oeis4.)