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
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.
Programs
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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 *)
Comments