A392239 - OEIS

%I #10 Jan 07 2026 08:39:34

%S 313,111,212,414,616,40140,28128,76176,1841184,60160,4001400,9201920,

%T 126411264,6641664,280012800,11614111614,894418944,40288140288,

%U 74080174080,24928124928,4827521482752,2206081220608,196032011960320,7448961744896,222246412222464,34873088134873088,300889613008896,720320017203200

%N 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.

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

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

%p N:= 30: # for a(1)..a(N)

%p V:= Vector(N): count:= 0:

%p t:= 10:

%p for x from 1 while count < N do

%p   if x = t then t:= 10*t fi;

%p   y:= x*(10*t+1)+t;

%p   v:= NumberTheory:-Omega(y);

%p   if v <= N and V[v] = 0 then V[v]:= y; count:= count+1 fi;

%p od:

%p convert(V,list);

%o (Python)

%o from sympy import factorint

%o from itertools import count, islice

%o def b(n): return 10**len(str(n))*(10*n+1) + n  # A392225

%o def agen(): # generator of terms

%o     n, adict = 1, dict()

%o     for t in (b(n) for n in count(1)):

%o         v = sum(factorint(t).values())

%o         if v not in adict:

%o             adict[v] = t

%o             while n in adict: yield adict[n]; n += 1

%o print(list(islice(agen(), 17))) # _Michael S. Branicky_, Jan 04 2026

%Y Cf. A001222, A392225, A392226, A392227.

%K nonn,base

%O 1,1

%A _Robert Israel_, Jan 04 2026