A237913 Smallest number m > 1 (not ending in a 0) such that m and the digit reversal of m have n prime factors (counted with multiplicity). Palindromes are included.

2, 4, 8, 88, 252, 2576, 21708, 2112, 4224, 8448, 44544, 48384, 2977792, 21989376, 405504, 4091904, 441606144, 405909504, 886898688, 677707776, 4285005824, 276486684672, 21128282112, 633498894336, 2701312131072, 6739855589376, 29142024192, 65892155129856, 4815463645184, 445488555884544

Offset: 1

Author

Derek Orr, Feb 15 2014

Keywords

• nonn
• base

Examples

			252 is the smallest number such that 252 and its reverse (also 252) have 5 prime factors (2*2*3*3*7). So, a(5) = 252.
2576 is the smallest number such that 2576 and its reverse (6752) have 6 prime factors (2*2*2*2*7*23 and 2*2*2*2*2*211, respectively). So a(6) = 2576.
		

Crossrefs

Cf. A004086, A076886, A237912.

Programs

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 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
x = 1
while x < 100:
  print(RevFact(x))
  x += 1

Formula

a(n) = min{A076886(n+1), A237912(n)}

Extensions

a(17)-a(21) from Giovanni Resta, Feb 23 2014

a(22)-a(30) from Max Alekseyev, Feb 08 2024