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A302575
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Numbers x which are the concatenation of y and the product of the digits of y.
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1
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11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 200, 212, 224, 236, 248, 300, 313, 326, 339, 400, 414, 428, 500, 515, 600, 616, 700, 717, 800, 818, 900, 919, 1000, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090, 1100
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OFFSET
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1,1
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LINKS
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EXAMPLE
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100 => 1*0 = 0; 326 => 3*2 = 6; 127798 => 1*2*7*7 = 98.
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MAPLE
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P:=proc(n) local k, ok; ok:=0; for k from 1 to ilog10(n) do
if convert(convert(trunc(n/10^k), base, 10), `*`)=n mod 10^k then ok:=1; break; fi; od;
if ok=1 then if n<100 or k<ilog10(n) then n; fi; fi; end: seq(P(i), i=1..1100);
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PROG
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(PARI) isok(n) = {d = digits(n); for (k=1, #d-1, da = vector(k, i, d[i]); db = vector(#d-k, i, d[k+i]); na = fromdigits(da); nb = fromdigits(db); if ((nb && db[1] != 0) || (nb==0), if (prod(j=1, k, da[j]) == nb, return (1)); ); ); } \\ Michel Marcus, Apr 13 2018
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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