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A232185
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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
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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945 is in the sequence because 9/45 + 94/5 = 19 is integer.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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