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A335645 Smallest palindrome with exactly n distinct prime factors. 2
1, 2, 6, 66, 858, 6006, 222222, 20522502, 244868442, 6172882716, 231645546132, 49795711759794, 2415957997595142, 495677121121776594, 22181673755737618122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

max{A002110(n), A076886(n), A239696(n)} <= a(n) <= A046399(n).

No more terms with less than 17 digits.

Next term: 10^16 <= a(13) <= 495677121121776594.

LINKS

Table of n, a(n) for n=0..14.

EXAMPLE

a(3)=66 because 66 is the smallest palindromic number with 3 distinct prime factors, 2*3*11.

PROG

(Python)

from sympy import factorint

def A335645(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 len(factorint(m)) == n:

        return m

    d += 1

print([A335645(n) for n in range(8)]) # Michael S. Branicky, Oct 02 2020

CROSSREFS

Subsequence of A002113.

Cf. A002110, A046399, A076886, A239696.

Sequence in context: A262047 A280393 A239696 * A082619 A046399 A082617

Adjacent sequences:  A335642 A335643 A335644 * A335646 A335647 A335648

KEYWORD

nonn,base,hard,more

AUTHOR

Michael S. Branicky, Oct 02 2020

EXTENSIONS

a(13) from Michael S. Branicky and David A. Corneth, Oct 03 2020

a(14) from David A. Corneth, Oct 03 2020

STATUS

approved

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Last modified January 28 22:30 EST 2022. Contains 350669 sequences. (Running on oeis4.)