A046330 -id:A046330 - cp's OEIS frontend

A046394 Palindromes with exactly 4 distinct prime factors.

858, 2002, 2442, 3003, 4774, 5005, 5115, 6666, 10101, 15351, 17871, 22422, 22722, 24242, 26562, 26962, 28482, 35853, 36363, 41314, 43734, 43834, 45654, 47874, 49494, 49794, 49894, 51015, 51315, 51415, 53535, 53835, 53935, 56865, 58485

Offset: 1

Patrick De Geest, Jun 15 1998

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A046330, A046410.

filter:= proc(n) local F;
  F:= ifactors(n)[2];
  nops(F)=4 and max(map(t->t[2],F))=1
end proc:
makepali:= proc(n,d) local L;
  L:= convert(n,base,10);
  if d::even then 10^(d/2)*n + add(L[i]*10^(d/2-i),i=1..d/2)
  else 10^((d-1)/2)*n + add(L[i]*10^((d+1)/2-i),i=2..(d+1)/2)
  fi
end proc:
select(filter, [seq(seq(makepali(x,d),
   x=10^ceil(d/2-1)..10^ceil(d/2)-1),d=1..6)]); # Robert Israel, Jun 05 2018

Select[Range[60000],PalindromeQ[#]&&PrimeNu[#]==Total[FactorInteger[#][[All,2]]] == 4&] (* Harvey P. Dale, Apr 07 2022 *)

A046410 Palindromes with exactly 4 distinct palindromic prime factors.

Original entry on oeis.org

6666, 22888822, 66888866, 413979314, 2228668222, 2668668662, 2888668882, 3315115133, 6668228666, 200446644002, 222266662222, 222446644222, 224488884422, 228866668822, 244666666442, 246664466642, 246686686642

Offset: 1

Patrick De Geest, Jun 15 1998

Cf. A046330, A046378.

a(10)-a(17) from Donovan Johnson, Jul 20 2010

A046378 Palindromes with exactly 4 palindromic prime factors (counted with multiplicity).

Original entry on oeis.org

88, 484, 525, 686, 808, 2662, 3773, 3993, 4444, 6666, 9999, 14641, 24442, 34643, 36663, 40804, 52525, 134431, 224422, 336633, 1234321, 1596951, 2060602, 3090903, 11333311, 14699641, 22888822, 66888866, 104060401, 125888521, 134969431, 367888763, 413979314

Offset: 1

Patrick De Geest, Jun 15 1998

			The palindrome 1596951 is a term since it has 4 factors 3^2 191 929, all palindromic.

Lars Blomberg, Table of n, a(n) for n = 1..320, terms < 10^16.

Cf. A046330, A046410.

More terms from Lars Blomberg, Nov 06 2015

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

Original entry on oeis.org

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

Hugo Pfoertner, Oct 25 2021

Cf. A001222, A002113, A046399, A335645.

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

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 *)

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

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

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A046394 Palindromes with exactly 4 distinct prime factors.

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A046410 Palindromes with exactly 4 distinct palindromic prime factors.

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A046378 Palindromes with exactly 4 palindromic prime factors (counted with multiplicity).

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

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