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

1,2

Links

Table of n, a(n) for n=1..25.

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 *)

Prog

(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

Crossrefs

Cf. A001222, A002113, A046399, A335645.

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

Sequence in context: A322614 A089337 A088114 * A239697 A237913 A076886

Adjacent sequences: A348047 A348048 A348049 * A348051 A348052 A348053

Keyword

nonn,base

Author

Hugo Pfoertner, 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

Status

approved