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.

111, 122, 133, 144, 155, 166, 177, 188, 199, 212, 224, 236, 248, 313, 326, 339, 414, 428, 515, 616, 717, 818, 919, 2510, 2612, 2714, 2816, 2918, 3412, 3515, 3618, 3721, 3824, 3927, 4312, 4416, 4520, 4624, 4728, 4832, 4936, 5210, 5315, 5420, 5525, 5630, 5735

Offset: 1

Author

Randy L. Ekl, Jan 06 2017

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A088294, A280636.

Programs

Maple

read("transforms") : # implements digcatL
isA280635 := proc(n)
    local dgs,spl1,spl2,dgs1,dgs2,dgs3;
    dgs := convert(n,base,10) ;
    if nops(dgs) >= 3 then
        for spl1 from 1 to nops(dgs)-2 do
        for spl2 from spl1+1 to nops(dgs)-1 do
            if op(-1,dgs) <> 0 and op(spl1,dgs) <> 0 and op(spl2,dgs) <> 0 then
                dgs1 := ListTools[Reverse]([op(spl2+1..nops(dgs),dgs)]) ;
                dgs2 := ListTools[Reverse]([op(spl1+1..spl2,dgs)]) ;
                dgs3 := ListTools[Reverse]([op(1..spl1,dgs)]) ;
                if digcatL(dgs1)*digcatL(dgs2) = digcatL(dgs3) then
                    return true;
                end if
            end if;
        end do:
        end do:
        false ;
    else
        false;
    end if;
end proc:
for n from 100 do
    if isA280635(n) then
        printf("%d,\n",n) ;
    end if;
end do: # R. J. Mathar, Jan 10 2017

Mathematica

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 *)