login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A256518 Consider numbers n = concat(x,y,z) such that the product x*y*z | n. Leading zeros in y and z allowed. Sequence lists numbers that admit different concatenations. 4
2112, 4224, 11110, 13104, 16128, 17136, 21120, 23184, 27216, 32256, 42240, 70224, 76608, 79632, 92736, 100128, 101101, 101808, 110110, 111100, 111375, 127008, 130104, 131040, 161280, 170170, 171360, 200112, 211200, 231840, 272160, 301125, 322560, 391092, 422400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n belongs to the sequence also n*10^k does.

Two concatenations are considered different when one of them is not a permutation of the other. E.g.: (6,2,22,5) and (6,22,2,5) are not different.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100

EXAMPLE

Only 2 or 3 different concatenations.

Two different concatenations:

92736 = concat(9*2*736) and 92736 / (9*2*736) = 7;

92736 = concat(92*7*36) and 92736 / (92*7*36) = 4.

Three different concatenations:

23184 = concat(2,3,184) and 23184 / (2*3*184) = 21;

23184 = concat(23,1,84) and 23184 / (23*1*84) = 12;

23184 = concat(23,18,4) and 23184 / (23*18*4) = 14.

The six concatenations of 111111 are excluded because they are basically just one: 1*11*111; 1*111*11; 11*1*111; 11*111*1; 111*1*11; 111*11*1 and 111111 / (1*11*111) = 91.

MAPLE

with(numtheory); P:=proc(q) local a, ab, b, c, i, j, k, m, n, v, w;

v:=array(1..10, 1..3); w:=[]; for n from 1 to q do j:=0;

for i from 1 to ilog10(n) do c:=(n mod 10^i); ab:=trunc(n/10^i);

for k from 1 to ilog10(ab) do a:=trunc(ab/10^k); b:=ab-a*10^k;

if a*b*c>0 then if type(n/(a*b*c), integer) then j:=j+1;

w:=sort([a, b, c]); for m from 1 to 3 do v[j, m]:=w[m]; od;

for m from 1 to j-1 do if v[m, 1]=v[j, 1] and v[m, 2]=v[j, 2] and v[m, 3]=v[j, 3]

then j:=j-1; break; fi; od; fi; fi; od; od;

if j>1 then print(n); fi; od; end: P(10^9);

MATHEMATICA

fQ[n_] := Block[{id = IntegerDigits@ n}, lng = Length@ id; t = Times @@@ Union[Sort /@ Partition[ Flatten@ Table[{FromDigits@ Take[id, {1, i}], FromDigits@ Take[id, {i + 1, j}], FromDigits@ Take[id, {j + 1, lng}]}, {i, 1, lng - 2}, {j, i + 1, lng - 1}], 3]]; Count[IntegerQ /@ (n/t), True] > 1]; k = 100; lst = {}; While[k < 1000001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Apr 09 2015 *)

CROSSREFS

Cf. A007602, A255725, A255726.

Sequence in context: A146895 A300008 A068343 * A046334 A046382 A168662

Adjacent sequences:  A256515 A256516 A256517 * A256519 A256520 A256521

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Apr 01 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)