A348050 Palindromes setting a new record of their number of prime divisors A001222.

1, 2, 4, 8, 88, 252, 2112, 4224, 8448, 44544, 48384, 405504, 4091904, 405909504, 677707776, 4285005824, 21128282112, 29142024192, 4815463645184, 445488555884544, 27874867776847872, 40539458585493504, 63556806860865536, 840261068860162048, 4870324782874230784

Offset: 1

Author

Hugo Pfoertner, Oct 25 2021

Keywords

• nonn
• base

Crossrefs

Cf. A001222, A002113, A046399, A335645.

Cf. A046328, A046329, A046330, A046331, A046332, A046333, A046334, A046335, A046336.

Programs

Mathematica

m=0;lst=Union@Flatten[Table[{FromDigits@Join[s=IntegerDigits@n,Reverse@s],FromDigits@Join[w=IntegerDigits@n,Rest@Reverse@w]},{n,10^5}]];Do[t=PrimeOmega@lst[[n]];If[t>m,Print@lst[[n]];m=t],{n,Length@lst}] (* Giorgos Kalogeropoulos, Oct 25 2021 *)

Python

from sympy import factorint
from itertools import product
def palsthru(maxdigits):
    midrange = [[""], [str(i) for i in range(10)]]
    for digits in range(1, maxdigits+1):
        for p in product("0123456789", repeat=digits//2):
            left = "".join(p)
            if len(left) and left[0] == '0': continue
            for middle in midrange[digits%2]:
                yield int(left+middle+left[::-1])
def afind(maxdigits):
    record = -1
    for p in palsthru(maxdigits):
        f = factorint(p, multiple=True)
        if p > 0 and len(f) > record:
            record = len(f)
            print(p, end=", ")
afind(10) # Michael S. Branicky, Oct 25 2021

Extensions

a(1) = 1 from David A. Corneth, Oct 25 2021

a(16)-a(19) from Giorgos Kalogeropoulos, Oct 25 2021

a(20) from Michael S. Branicky, Oct 25 2021

a(21)-a(25) from Chai Wah Wu, Oct 28 2021