|
Search: id:A113756
|
|
|
| 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. |
|
+0
1
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
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: A136446 A074726 A091013 this_sequence A055482 A076485 A071354
Adjacent sequences: A113753 A113754 A113755 this_sequence A113757 A113758 A113759
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 17 2006
|
|
|
Search completed in 0.002 seconds
|
