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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 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.)