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%I #22 Oct 28 2021 17:39:54
%S 1,2,4,8,88,252,2112,4224,8448,44544,48384,405504,4091904,405909504,
%T 677707776,4285005824,21128282112,29142024192,4815463645184,
%U 445488555884544,27874867776847872,40539458585493504,63556806860865536,840261068860162048,4870324782874230784
%N Palindromes setting a new record of their number of prime divisors A001222.
%t 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 *)
%o (Python)
%o from sympy import factorint
%o from itertools import product
%o def palsthru(maxdigits):
%o midrange = [[""], [str(i) for i in range(10)]]
%o for digits in range(1, maxdigits+1):
%o for p in product("0123456789", repeat=digits//2):
%o left = "".join(p)
%o if len(left) and left[0] == '0': continue
%o for middle in midrange[digits%2]:
%o yield int(left+middle+left[::-1])
%o def afind(maxdigits):
%o record = -1
%o for p in palsthru(maxdigits):
%o f = factorint(p, multiple=True)
%o if p > 0 and len(f) > record:
%o record = len(f)
%o print(p, end=", ")
%o afind(10) # _Michael S. Branicky_, Oct 25 2021
%Y Cf. A001222, A002113, A046399, A335645.
%Y Cf. A046328, A046329, A046330, A046331, A046332, A046333, A046334, A046335, A046336.
%K nonn,base
%O 1,2
%A _Hugo Pfoertner_, Oct 25 2021
%E a(1) = 1 from _David A. Corneth_, Oct 25 2021
%E a(16)-a(19) from _Giorgos Kalogeropoulos_, Oct 25 2021
%E a(20) from _Michael S. Branicky_, Oct 25 2021
%E a(21)-a(25) from _Chai Wah Wu_, Oct 28 2021
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