A336399 a(1) = 1, a(n) is the smallest number such that the concatenation a(1)a(2)...a(n) is divisible by lcm(1..n).

1, 0, 2, 0, 0, 0, 360, 0, 1680, 0, 35280, 0, 332640, 0, 0, 0, 8648640, 0, 306306000, 0, 0, 0, 232792560, 0, 0, 0, 26771144400, 0, 481880599200, 0, 41923612130400, 0, 0, 0, 0, 0, 5487335009956800, 0, 0, 0, 245774847024907200, 0, 8105227020364874400, 0, 0, 0, 452140231622516236800, 0, 3984485791173424336800, 0

Offset: 1

Author

Eder Vanzei, Jul 20 2020

Keywords

• base
• nonn

Examples

			a(7) = 360 as the smallest positive integer k such that the concatenation a(1)a(2)..a(6)k is divisible by lcm(1..7) = 420. - _David A. Corneth_, Jul 21 2020
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2297
• David A. Corneth, PARI program

Crossrefs

Cf. A336401 (corresponding numbers), A003418 (LCM's).

Cf. A045874, A051883, A078282, A078283, A214437.

Programs

Maple

N:= 1: R:= 1: C:= 1:
for n from 2 to 60 do
  N:= ilcm(N,n);
  for d from 1 do
    x:= -C*10^d mod N;
    if x = 0 then lx:= 1 else lx:= 1+ilog10(x) fi;
    if lx = d then
       R:= R,x;
       C:= C*10^d+x;
       break
    elif lx < d then
       k:= ceil((10^(d-1)-x)/N);
       x:= x + k*N;
       if x < 10^d then
         R:= R,x;
         C:= C*10^d+x;
         break
    fi fi
od; od:
R; # Robert Israel, Sep 16 2020

PARI

a(n) = {if(n==1,return(1));for(n1 = 0, oo, ; k[n]=eval(concat(Str(k[n-1]), n1)); n2=0; for(n3 = 1, n, if(k[n] % n3 == 0, n2+=1; if(n2==n, return(k[n])))))};
k = vector(10000);print1(k[1]=1,", ");for(j=1, 20, print1(a(j+1) - a(j)*10^(length(Str(a(j+1))) - length(Str(a(j)))), ", "))

PARI

\\ See Corneth link. David A. Corneth, Jul 21 2020

Extensions

a(27)-a(50) from David A. Corneth, Jul 20 2020