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 A232184 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. 1
 11, 21, 22, 31, 33, 41, 42, 44, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 101, 201, 202, 301, 303, 401, 402, 404, 501, 505, 601, 602, 603, 606, 612, 701, 707, 801, 802, 804, 808, 816, 901, 903, 909, 945, 1001, 1003, 1011, 2001, 2002, 2003 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A084906(n) for n = 1..24. 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, 11, 22, 11, 33, 11, 44, 22,... 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 11 to 3000 do: x:=convert(n, base, 10):n1:=nops(x):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:od: CROSSREFS Cf. A084906. Sequence in context: A084854 A108237 A084906 * A232185 A118853 A117841 Adjacent sequences:  A232181 A232182 A232183 * A232185 A232186 A232187 KEYWORD nonn,base AUTHOR Michel Lagneau, Nov 20 2013 STATUS approved

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Last modified April 16 23:40 EDT 2021. Contains 343051 sequences. (Running on oeis4.)