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

1,1

Links

Table of n, a(n) for n=1..52.

Example

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

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<ilog10(n) then n; fi; fi; end: seq(P(i), i=1..1100);

Prog

(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

Crossrefs

Cf. A007954, A108203.

Sequence in context: A044851 A276769 A160861 * A302801 A067042 A078273

Adjacent sequences: A302572 A302573 A302574 * A302576 A302577 A302578

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 10 2018

Status

approved