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

2, 6, 66, 858, 6006, 204204, 10444434, 208888680, 6172882716, 231645546132, 49795711759794, 2400532020354468, 477566276048801940, 24333607174192936620

Offset: 1

Author

Derek Orr, Mar 24 2014

Keywords

• nonn
• base
• more

Comments

a(15) > 10^21. - Max Alekseyev, Feb 16 2024

Examples

			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.
		

Crossrefs

Cf. A046399, A113548.

Programs

PARI

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)));
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

Python

import sympy
from sympy import factorint
def Rev(x):
  rev = ''
  for i in str(x):
    rev = i + rev
  return int(rev)
def RevFact(x):
  n = 2
  while n < 10**8:
    if len(list(factorint(n).values())) == x:
      if len(list(factorint(Rev(n)).values())) == x:
        return n
      else:
        n += 1
    else:
      n += 1
x = 1
while x < 50:
  print(RevFact(x))
  x += 1

Extensions

a(8)-a(9) from Giovanni Resta, Mar 28 2014

a(10)-a(12) from Daniel Suteu, Feb 07 2023

a(13) from Michael S. Branicky, Feb 14 2023

a(14) from Max Alekseyev, Feb 15 2024