A392239 a(n) is the least number with exactly n prime factors, counted with multiplicity, that is the concatenation of x, 1, and x for some x.

313, 111, 212, 414, 616, 40140, 28128, 76176, 1841184, 60160, 4001400, 9201920, 126411264, 6641664, 280012800, 11614111614, 894418944, 40288140288, 74080174080, 24928124928, 4827521482752, 2206081220608, 196032011960320, 7448961744896, 222246412222464, 34873088134873088, 300889613008896, 720320017203200

Offset

1,1

Comments

a(n) is the least member k of A392225 such that A001222(k) = n.

Links

Table of n, a(n) for n=1..28.

Example

a(3) = 212 because 212 = 2*2*53.

Maple

N:= 30: # for a(1)..a(N)
V:= Vector(N): count:= 0:
t:= 10:
for x from 1 while count < N do
  if x = t then t:= 10*t fi;
  y:= x*(10*t+1)+t;
  v:= NumberTheory:-Omega(y);
  if v <= N and V[v] = 0 then V[v]:= y; count:= count+1 fi;
od:
convert(V, list);

Prog

(Python)
from sympy import factorint
from itertools import count, islice
def b(n): return 10**len(str(n))*(10*n+1) + n  # A392225
def agen(): # generator of terms
    n, adict = 1, dict()
    for t in (b(n) for n in count(1)):
        v = sum(factorint(t).values())
        if v not in adict:
            adict[v] = t
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 17))) # Michael S. Branicky, Jan 04 2026

Crossrefs

Cf. A001222, A392225, A392226, A392227.

Sequence in context: A234624 A292197 A083972 * A045275 A238057 A097023

Adjacent sequences: A392236 A392237 A392238 * A392240 A392241 A392242

Keyword

nonn,base

Author

Robert Israel, Jan 04 2026

Status

approved