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

0,2

Comments

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

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

Example

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

Prog

(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

Crossrefs

Cf. A239697.

Sequence in context: A348050 A239697 A237913 * A309565 A046385 A068664

Adjacent sequences: A076883 A076884 A076885 * A076887 A076888 A076889

Keyword

base,nonn

Author

Shyam Sunder Gupta, Nov 25 2002

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

Status

approved