OFFSET
1,1
COMMENTS
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 1000 terms from Paolo P. Lava)
EXAMPLE
15 = concat(1,5); 1*5 = 5 and 15 / 5 = 3.
36 = concat(3,6); 3*6 = 18 and 36 / 18 = 2.
9072 = concat(9,072); 9*72 = 648 and 9072 / 648 = 14.
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 a*b>0 then if type(n/(a*b), integer) then print(n);
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 && 0 < 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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Apr 01 2015
STATUS
approved