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%I #2 Mar 30 2012 17:40:33
%S 12,18,24,35,50,56,90,100,120,180,210,315,350,450,500,672,728,780,840,
%T 910,1500,1800,3150,3500,3920,4320,4752,5000,7056,7200,7744,8960,
%U 16500,18000,19008,24960,31500,35000,50000,57915,59400,60480,67392,91728
%N Numbers n>9 such that n=Abs[(c+d_1)*(c+d_2)*...*(c+d_k)] where d_1 d_2 ... d_k is the decimal expansion of n and c is an integer constant.
%C Some entries, namely 12, 18, 24, 35, 50, 56, 90, 120, 210, 315, 840, 4752, 7744, 917280 (up to 10^20), have 2 representations, e.g., 840 for c=6 and c=-14 or 917280 for c=6 and c=-15. Sequence is infinite since contains 35*10^k, 315*10^k, 18*10^k and 5*10^k, for k>=0 and c=-10.
%e 315 belongs since 315=|(4+3)(4+1)(4+5)|
%e 728 belongs since 728=|(-15+7)(-15+2)(-15+8)|
%t L = {}; Do[d = IntegerDigits@n; Do[If[n == Abs[Times @@ (d + c)], AppendTo[L, {n, c}]; Print[{n, c}]], {c, -19, 10}], {n, 10, 1000000}]; Print[Union[Transpose[L][[1]]]]; L
%Y Cf. A055482, A115227, A098113, A098114, A097371, A097372.
%K base,nonn
%O 1,1
%A _Giovanni Resta_, Jan 17 2006
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