cp's OEIS Frontend

A280635 Numbers whose digit string can be partitioned into three nonempty parts such that the product of the first two parts equals the third part.

%I A280635 #28 Jan 10 2017 07:18:18
%S A280635 111,122,133,144,155,166,177,188,199,212,224,236,248,313,326,339,414,
%T A280635 428,515,616,717,818,919,2510,2612,2714,2816,2918,3412,3515,3618,3721,
%U A280635 3824,3927,4312,4416,4520,4624,4728,4832,4936,5210,5315,5420,5525,5630,5735
%N A280635 Numbers whose digit string can be partitioned into three nonempty parts such that the product of the first two parts equals the third part.
%C A280635 Could be called "area numbers" since if the first set of digits is the length, and the second set of digits is the width, then the last set of digits is the area, with length * width = area.
%e A280635 236 is in the sequence since 2*3=6. 3515 is in the sequence since 3*5=15. Leading zeros are not allowed, thus 2036 (2*03=6) is not included.
%p A280635 read("transforms") : # implements digcatL
%p A280635 isA280635 := proc(n)
%p A280635     local dgs,spl1,spl2,dgs1,dgs2,dgs3;
%p A280635     dgs := convert(n,base,10) ;
%p A280635     if nops(dgs) >= 3 then
%p A280635         for spl1 from 1 to nops(dgs)-2 do
%p A280635         for spl2 from spl1+1 to nops(dgs)-1 do
%p A280635             if op(-1,dgs) <> 0 and op(spl1,dgs) <> 0 and op(spl2,dgs) <> 0 then
%p A280635                 dgs1 := ListTools[Reverse]([op(spl2+1..nops(dgs),dgs)]) ;
%p A280635                 dgs2 := ListTools[Reverse]([op(spl1+1..spl2,dgs)]) ;
%p A280635                 dgs3 := ListTools[Reverse]([op(1..spl1,dgs)]) ;
%p A280635                 if digcatL(dgs1)*digcatL(dgs2) = digcatL(dgs3) then
%p A280635                     return true;
%p A280635                 end if
%p A280635             end if;
%p A280635         end do:
%p A280635         end do:
%p A280635         false ;
%p A280635     else
%p A280635         false;
%p A280635     end if;
%p A280635 end proc:
%p A280635 for n from 100 do
%p A280635     if isA280635(n) then
%p A280635         printf("%d,\n",n) ;
%p A280635     end if;
%p A280635 end do: # _R. J. Mathar_, Jan 10 2017
%t A280635 With[{nn = 1}, Union@ Flatten@ Table[FromDigits@ Flatten@ Map[IntegerDigits, {n, k, n k}], {n, 10^nn - 1}, {k, 10^nn - 1}]] (* _Michael De Vlieger_, Jan 07 2017 *)
%Y A280635 Cf. A088294, A280636.
%K A280635 nonn,base
%O A280635 1,1
%A A280635 _Randy L. Ekl_, Jan 06 2017