A376153 - OEIS

%I #4 Sep 13 2024 08:07:08

%S 13,115,1113,11116,1111124,11111120,111111156,1111111128,11111111616,

%T 111111121116,1111111111616,111111111113184,1111111111113012,

%U 11111111111112192,111111111111151616,1111111111111113216,51111111111111111168,111411111111111111168,11111111111111111311360

%N a(n) is the least number with n decimal digits 1 and n prime factors, counted with multiplicity.

%e a(3) = 1113 because 1113 contains 3 1's and 1113 = 3 * 7 * 53 has 3 prime factors, counted with multiplicity.

%p g:= proc(x,S,d)

%p local L,i;

%p   L:= convert(x,base,9);

%p   add(`if`(L[i]=0,0,L[i]+1)*10^S[i],i=1..nops(L)) + add(10^i,i={$0..d-1} minus S)

%p end proc:

%p f:= proc(n)

%p     local x,d,Cands,S;

%p     x:= (10^n-1)/9;

%p     if numtheory:-bigomega(x) = n then return x fi;

%p     for d from n+1 do

%p       Cands:= sort([seq(seq(g(x,S,d),x =9^(d-n-1) .. 9^(d-n)-1),S = combinat:-choose({$0..d-1},d-n))]);

%p       for x in Cands do if numtheory:-bigomega(x) = n then return x fi od;

%p     od;

%p end proc:

%p seq(f(i),i=1..19);

%Y Cf. A376063.

%K nonn,base

%O 1,1

%A _Robert Israel_, Sep 12 2024