A302575 Numbers x which are the concatenation of y and the product of the digits of y.

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

Offset: 1

Author

Paolo P. Lava, Apr 10 2018

Keywords

• nonn
• base
• easy

Examples

			100 => 1*0 = 0; 326 => 3*2 = 6; 127798 => 1*2*7*7 = 98.
		

Crossrefs

Cf. A007954, A108203.

Programs

Maple

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
				

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