A076886 Smallest palindrome with exactly n prime factors (counted with multiplicity).

1, 2, 4, 8, 88, 252, 2772, 27872, 2112, 4224, 8448, 44544, 48384, 2977792, 27011072, 405504, 4091904, 441606144, 405909504, 886898688, 677707776, 4285005824, 276486684672, 21128282112, 633498894336, 2701312131072, 6739855589376, 29142024192, 65892155129856

Offset: 0

Author

Shyam Sunder Gupta, Nov 25 2002

Keywords

• base
• nonn

Comments

2^n <= A239697(n) <= a(n). - Michael S. Branicky, Oct 02 2020

Examples

			a(4)=88 because 88 is the smallest palindromic number with 4 prime factors, 2^3*11 (counted with multiplicity).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..30 from Michael S. Branicky and terms 31..35 from David A. Corneth)
• Andrew Howroyd, PARI Program

Crossrefs

Cf. A239697.

Programs

Python

from sympy import factorint
def A076886(n):
  d = 1
  while True:
    half = (d+1)//2
    for left in range(10**(half-1), 10**half):
      strleft = str(left)
      if d%2 == 0:
        m = int(strleft + strleft[::-1])
      else:
        m = int(strleft + (strleft[:-1])[::-1])
        if sum(list(factorint(m).values())) == n:
          return m
    d += 1
print([A076886(n) for n in range(17)]) # Michael S. Branicky, Oct 02 2020

Extensions

Edited and extended by Robert G. Wilson v, Dec 02 2002

a(26) corrected and a(27)-a(28) from Michael S. Branicky, Oct 02 2020