This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A255726 Numbers n = concat(x,y) such that the product x*y | n. No leading zeros in y allowed. 5
 11, 12, 15, 24, 36, 110, 120, 125, 150, 240, 315, 360, 735, 1100, 1125, 1200, 1250, 1352, 1500, 1734, 2400, 3150, 3375, 3600, 7350, 11000, 11250, 12000, 12500, 13520, 14112, 15000, 17340, 18144, 21168, 24000, 31500, 33750, 36000, 42336, 63504, 67335, 73500, 91125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subset of A255725. Values of the ratio n / (x*y) are 2, 3, 5, 6, 7, 9 and 11. There are numbers that present an additional quasi-solution. For instance consider 26733375: it is in the sequence because 26733375 / (267 * 33375) = 3 but 26733375 / (2673337 * 5) = 2.000000374... is close to being an integer, too. Other examples: 52116672 / (521 * 16672) = 6 and 52116672 / (5211667 * 2) = 5.000000191... 138911112 / (1389 * 11112) = 9 and 138911112 / (13891111 * 2) = 5.0000000719... Is there any number that admits two or more different concatenations whose multiplications divide the number itself (no term up to 3*10^9)? LINKS Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 200 terms from Paolo P. Lava) EXAMPLE 11 = concat(1,1); 1*1 = 1 and 11 / 1 = 11. 12 = concat(3,6); 1*2 = 2 and 12 / 2 = 6. 240 = concat(2,40); 2*40 = 80 and 240 / 80 = 3. MAPLE with(numtheory); P:=proc(q) local a, b, i, n; for n from 1 to q do for i from 1 to ilog10(n) do a:=trunc(n/10^i);  b:=n-a*10^i; if i=ilog10(b)+1 then if a*b>0 then if type(n/(a*b), integer) then print(n); fi; fi; fi; od; od; end: P(10^9); MATHEMATICA v[e_]:=Block[{x, y, k}, y+10^e*x /. List@ ToRules@ Reduce[k*x*y ==  x*10^e+y && k>=0 && x>0 && 10^(e-1) <= y < 10^e, {k, x, y}, Integers]]; upto[nd_] := Select[ Union@ Flatten@ Array[v, nd], # < 10^nd &]; upto[10] (* terms < 10^10, Giovanni Resta, May 26 2015 *) CROSSREFS Cf. A007602, A255725, A256518. Sequence in context: A113600 A255725 A287442 * A097158 A072239 A079350 Adjacent sequences:  A255723 A255724 A255725 * A255727 A255728 A255729 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.

Last modified June 19 04:44 EDT 2019. Contains 324217 sequences. (Running on oeis4.)