|
%I #4 Nov 21 2013 13:01:07
%S 11,21,22,31,33,41,42,44,51,55,61,62,63,66,71,77,81,82,84,88,91,93,99,
%T 101,201,202,301,303,401,402,404,501,505,601,602,603,606,612,701,707,
%U 801,802,804,808,816,901,903,909,945,1001,1003,1011,2001,2002,2003
%N 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.
%C a(n) = A084906(n) for n = 1..24.
%C 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,...
%e 945 is in the sequence because 9/45 + 94/5 = 19 is integer.
%p 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:
%Y Cf. A084906.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Nov 20 2013
|
