login
n-th number with exactly n n's in base 10.
0

%I #7 Jul 18 2015 21:55:51

%S 1,122,2333,34444,455555,5666666,67777777,788888888,8999999999,

%T 101010101010101010010,11111111110111111111111,

%U 1212121121212121212121212,131313013131313131313131313,14141241414141414141414141414

%N n-th number with exactly n n's in base 10.

%C Main diagonal M[n,n,n] of M[i,j,k] = k-th natural number such that number of i's in base 10 is j, for i,j,k = 1,2,3,4,5,....

%C M[1,1,n] = A043493 Numbers that contain a single 1.

%C M[2,2,n] = A043498 Numbers n such that number of 2's in base 10 is 2.

%C M[3,3,n] = A043503 Numbers n such that number of 3's in base 10 is 3.

%C M[4,4,n] = A043508 Numbers n such that number of 4's in base 10 is 4.

%e First element is 1, the 1st natural number with exactly one 1 in base 10.

%e Second element is 122, the 2nd natural number with exactly two 2's in base 10.

%e Third element is 2333, the 3rd natural number with exactly three 3's in base 10.

%o (PARI) a(n)=my(v=List(),k=10^#Str(n),d=List(digits((k^n-1)/(k-1)*n)),t); for(i=1,#d+1, t=d; listinsert(t,0,i); t=Vec(t); for(j=0,9, t[i]=j; listput(v,fromdigits(t)))); Set(v)[n] \\ _Charles R Greathouse IV_, Jun 29 2015

%Y Cf. A043493, A043498, A043503, A043508.

%K nonn,base,easy

%O 1,2

%A _Jonathan Vos Post_, Jun 29 2015

%E a(5)-a(14) from _Charles R Greathouse IV_, Jun 29 2015