A237913 -id:A237913 - cp's OEIS frontend

A237912 Smallest number m (not ending in a 0) such that m and its digit reversal A004086(m) both have n prime factors (counted with multiplicity).

13, 15, 117, 126, 1386, 2576, 21708, 25515, 21168, 46848, 295245, 2937856, 6351048, 21989376, 217340928, 2154281472, 2196652032, 21120051456, 21122906112, 40915058688, 274148425728, 2150086519296, 2707602702336, 6167442456576, 21907217055744, 29798871072768, 420127895977984

Offset: 1

Derek Orr, Feb 15 2014

Palindromes are not included in this sequence since the reverse of a palindrome is the same number. See A076886 and A237913.

			13 and 31 are both prime so a(1) = 13.
15 and 51 have two prime factors (3*5 and 3*17 respectively), so a(2) = 15.

Cf. A004086, A076886, A237913.

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 = 1
  while n < 10**8:
    if rev(n) != n:
      if n % 10 != 0:
        if sum(list(factorint(n).values())) == x:
          if sum(list(factorint(rev(n)).values())) == x:
            return n
          else:
            n += 1
        else:
          n += 1
      else:
        n += 1
    else:
      n += 1
x = 1
while x < 100:
  print(RevFact(x))
  x += 1

a(15)-a(21) from Giovanni Resta, Feb 23 2014

a(22)-a(27) from Max Alekseyev, Feb 07 2024

A239697 Smallest m such that m and reverse(m) each have n (not necessarily distinct) prime factors.

Original entry on oeis.org

2, 4, 8, 88, 252, 2576, 8820, 2112, 4224, 8448, 44544, 48384, 846720, 4078080, 405504, 4091904, 441606144, 405909504, 886898688, 677707776, 4285005824, 63769149440, 21128282112, 633498894336, 2701312131072, 6739855589376, 29142024192, 65892155129856, 4815463645184, 445488555884544, 23088546155855872

Offset: 1

Derek Orr, Mar 24 2014

For all terms thus far, both m and reverse(m) are even.

a(24) > 10^11. - Giovanni Resta, Mar 31 2014

			2576 = 2*2*2*2*23*7 (6 factors)
6752 = 2*2*2*2*2*211 (6 factors)
Since 2576 is the smallest number with this property, a(6) = 2576.

Cf. A237912, A237913.

A239697 := proc(n)
    local a;
    for a from 1 do
        if numtheory[bigomega](a) = n then
            if numtheory[bigomega](digrev(a)) =n then
                return a;
            end if;
        end if;
    end do:
end proc: # R. J. Mathar, Apr 04 2014

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

{min m: A001222(m) = A001222(A004086(m))}. - R. J. Mathar, Apr 04 2014

a(17)-a(23) from Giovanni Resta, Mar 31 2014

a(24)-a(31) from David A. Corneth, Oct 03 2020

cp's OEIS Frontend

A237912 Smallest number m (not ending in a 0) such that m and its digit reversal A004086(m) both have n prime factors (counted with multiplicity).

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