A388789 a(n) is the least number ending in at least n identical digits that has exactly n prime divisors, counted with multiplicity.

2, 22, 222, 4444, 88888, 222222, 18888888, 1455555555, 13888888888, 54444444444, 4788888888888, 336888888888888, 4011111111111111, 8022222222222222, 2769888888888888888, 269454444444444444444, 2375988888888888888888, 138816111111111111111111, 277632222222222222222222

Offset

1,1

Links

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

Example

a(7) = 18888888 because 18888888 = 2^3 * 3 * 19 * 23 * 1801 ends with 7 digits 8 and is the product of 7 primes, counted with multiplicity, and no smaller number works.
a(13) = 4011111111111111 ends in 14 identical digits; if "at least n" was replaced by "exactly n" in the definition, a(13) would be 12648888888888888.

Maple

f:= proc(n) local a, b, t, x;
  t:= (10^n-1)/9;
  for b from 0 do
    for a from 1 to 9 do
      x:= a*t + b*10^n;
      if numtheory:-bigomega(x) = n then return x fi;
  od od
end proc:
map(f, [$1..16]);

Prog

(Python)
from sympy import factorint
from itertools import count
def f(n): return sum(e for p, e in factorint(n).items())
def a(n):
    Rn, pow10 = (10**n-1)//9, 10**n
    return next(t for d in count(0) for r in range(10**(d-1) if d else 0, 10**d) for m in range(1, 10) if f(t:=r*pow10 + m*Rn) == n)
print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Sep 21 2025

Crossrefs

Cf. A376063.

Sequence in context: A002276 A374665 A384403 * A389187 A112893 A086855

Adjacent sequences: A388786 A388787 A388788 * A388790 A388791 A388792

Keyword

nonn,base

Author

Robert Israel, Sep 20 2025

Extensions

a(19) from Michael S. Branicky, Sep 21 2025

Status

approved