A113756 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.

12, 18, 24, 35, 50, 56, 90, 100, 120, 180, 210, 315, 350, 450, 500, 672, 728, 780, 840, 910, 1500, 1800, 3150, 3500, 3920, 4320, 4752, 5000, 7056, 7200, 7744, 8960, 16500, 18000, 19008, 24960, 31500, 35000, 50000, 57915, 59400, 60480, 67392, 91728

Offset: 1

Author

Giovanni Resta, Jan 17 2006

Keywords

• base
• nonn

Comments

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.

Examples

			315 belongs since 315=|(4+3)(4+1)(4+5)|
728 belongs since 728=|(-15+7)(-15+2)(-15+8)|
		

Crossrefs

Cf. A055482, A115227, A098113, A098114, A097371, A097372.

Programs

Mathematica

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