cp's OEIS Frontend

A239696 Smallest number m such that m and reverse(m) each have exactly n distinct prime factors.

%I A239696 #28 May 22 2025 10:21:37
%S A239696 2,6,66,858,6006,204204,10444434,208888680,6172882716,231645546132,
%T A239696 49795711759794,2400532020354468,477566276048801940,
%U A239696 24333607174192936620
%N A239696 Smallest number m such that m and reverse(m) each have exactly n distinct prime factors.
%C A239696 a(15) > 10^21. - _Max Alekseyev_, Feb 16 2024
%e A239696 The first nontrivial example is a(6) = 204204. 204204 = 2^2*3*7*11*13*17 (6 distinct prime factors). 402402 = 2*3*7*11*13*67 (6 distinct prime factors). Since 204204 is the smallest number with this property, a(6) = 204204.
%o A239696 (Python)
%o A239696 import sympy
%o A239696 from sympy import factorint
%o A239696 def Rev(x):
%o A239696   rev = ''
%o A239696   for i in str(x):
%o A239696     rev = i + rev
%o A239696   return int(rev)
%o A239696 def RevFact(x):
%o A239696   n = 2
%o A239696   while n < 10**8:
%o A239696     if len(list(factorint(n).values())) == x:
%o A239696       if len(list(factorint(Rev(n)).values())) == x:
%o A239696         return n
%o A239696       else:
%o A239696         n += 1
%o A239696     else:
%o A239696       n += 1
%o A239696 x = 1
%o A239696 while x < 50:
%o A239696   print(RevFact(x))
%o A239696   x += 1
%o A239696 (PARI)
%o A239696 generate(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), my(v=m*q); while(v <= B, if(j==1, if(v>=A && omega(fromdigits(Vecrev(digits(v)))) == n, listput(list, v)), if(v*(q+1) <= B, list=concat(list, f(v, q+1, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
%o A239696 a(n) = my(x=vecprod(primes(n)), y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ _Daniel Suteu_, Feb 07 2023
%Y A239696 Cf. A046399, A113548.
%K A239696 nonn,base,more
%O A239696 1,1
%A A239696 _Derek Orr_, Mar 24 2014
%E A239696 a(8)-a(9) from _Giovanni Resta_, Mar 28 2014
%E A239696 a(10)-a(12) from _Daniel Suteu_, Feb 07 2023
%E A239696 a(13) from _Michael S. Branicky_, Feb 14 2023
%E A239696 a(14) from _Max Alekseyev_, Feb 15 2024