A376153 a(n) is the least number with n decimal digits 1 and n prime factors, counted with multiplicity.

13, 115, 1113, 11116, 1111124, 11111120, 111111156, 1111111128, 11111111616, 111111121116, 1111111111616, 111111111113184, 1111111111113012, 11111111111112192, 111111111111151616, 1111111111111113216, 51111111111111111168, 111411111111111111168, 11111111111111111311360

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

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

Maple

g:= proc(x, S, d)
local L, i;
  L:= convert(x, base, 9);
  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)
end proc:
f:= proc(n)
    local x, d, Cands, S;
    x:= (10^n-1)/9;
    if numtheory:-bigomega(x) = n then return x fi;
    for d from n+1 do
      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))]);
      for x in Cands do if numtheory:-bigomega(x) = n then return x fi od;
    od;
end proc:
seq(f(i), i=1..19);

Crossrefs

Cf. A376063.

Sequence in context: A362514 A115188 A155621 * A232319 A296332 A021034

Adjacent sequences: A376150 A376151 A376152 * A376154 A376155 A376156

Keyword

nonn,base

Author

Robert Israel, Sep 12 2024

Status

approved