A388789 - OEIS

%I #19 Sep 25 2025 00:03:37

%S 2,22,222,4444,88888,222222,18888888,1455555555,13888888888,

%T 54444444444,4788888888888,336888888888888,4011111111111111,

%U 8022222222222222,2769888888888888888,269454444444444444444,2375988888888888888888,138816111111111111111111,277632222222222222222222

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

%e 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.

%e 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.

%p f:= proc(n) local a,b,t,x;

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

%p   for b from 0 do

%p     for a from 1 to 9 do

%p       x:= a*t + b*10^n;

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

%p   od od

%p end proc:

%p map(f, [$1..16]);

%o (Python)

%o from sympy import factorint

%o from itertools import count

%o def f(n): return sum(e for p, e in factorint(n).items())

%o def a(n):

%o     Rn, pow10 = (10**n-1)//9, 10**n

%o     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)

%o print([a(n) for n in range(1, 15)]) # _Michael S. Branicky_, Sep 21 2025

%Y Cf. A376063.

%K nonn,base

%O 1,1

%A _Robert Israel_, Sep 20 2025

%E a(19) from _Michael S. Branicky_, Sep 21 2025