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

1,1

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.

Links

Table of n, a(n) for n=1..44.

Example

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

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

Crossrefs

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

Sequence in context: A181941 A206449 A241852 * A055482 A284342 A362844

Adjacent sequences: A113753 A113754 A113755 * A113757 A113758 A113759

Keyword

base,nonn

Author

Giovanni Resta, Jan 17 2006

Status

approved