A046349 -id:A046349 - cp's OEIS frontend

A046351 Palindromic composite numbers with only palindromic prime factors.

4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 121, 202, 242, 252, 262, 303, 343, 363, 393, 404, 484, 505, 525, 606, 616, 626, 686, 707, 808, 909, 939, 1111, 1331, 1441, 1661, 1991, 2112, 2222, 2662, 2772, 2882, 3333, 3443, 3773, 3883, 3993, 4224, 4444, 5445

Offset: 1

Patrick De Geest, Jun 15 1998

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A002385, A032350, A033620, A046349, A046350.

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[4,5500],!PrimeQ[#]&&And@@palQ/@Join[{#},First/@FactorInteger[#]]&](* Jayanta Basu, Jun 05 2013 *)

from itertools import product
from sympy import isprime, primefactors as pf
def pal(n): s = str(n); return s == s[::-1]
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 okpal(p): return p > 3 and not isprime(p) and all(pal(f) for f in pf(p))
print(list(filter(okpal, palsthru(4)))) # Michael S. Branicky, Apr 06 2021

(A032350 INTERSECT A033620) MINUS {1}. - R. J. Mathar, Sep 09 2015

A046355 Composite numbers with only palindromic prime factors whose sum is palindromic (counted with multiplicity).

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 27, 28, 40, 45, 48, 54, 121, 308, 440, 495, 528, 594, 735, 784, 875, 882, 1050, 1120, 1250, 1260, 1331, 1344, 1500, 1512, 1600, 1701, 1800, 1920, 2025, 2048, 2101, 2121, 2160, 2304, 2430, 2525, 2592, 2751, 2916, 3030

Offset: 1

Patrick De Geest, Jun 15 1998

Subsequence of the numbers k in A046349 such that A262049(k) is in A002113. - R. J. Mathar, Sep 09 2015

			3030 = 2 * 3 * 5 * 101 -> 2 + 3 + 5 + 101 = 111 and 111 is a palindrome.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A046356, A046357.

isA046355 := proc(n)
    local sofpp ;
    if isA046349(n) then
        sofpp := A262049(n) ;
        isA002113(sofpp) ;
    else
        false;
    end if;
end proc:
for n from 2 to 400 do
    if isA046355(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Sep 09 2015

palQ[n_] := Reverse[x=IntegerDigits[n]] == x; Select[Range[4,3100], !PrimeQ[#] && And@@palQ/@Join[{Total[Times@@@(x=FactorInteger[#])]}, First/@x]&] (* Jayanta Basu, Jun 05 2013 *)

A046350 Odd composite numbers with only palindromic prime factors.

Original entry on oeis.org

9, 15, 21, 25, 27, 33, 35, 45, 49, 55, 63, 75, 77, 81, 99, 105, 121, 125, 135, 147, 165, 175, 189, 225, 231, 243, 245, 275, 297, 303, 315, 343, 363, 375, 385, 393, 405, 441, 453, 495, 505, 525, 539, 543, 567, 573, 605, 625, 655, 675, 693, 707, 729, 735, 755

Offset: 1

Patrick De Geest, Jun 15 1998

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A002385, A033620, A046349, A046351.

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[9,755,2],!PrimeQ[#]&&And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)
Select[Range[9,800,2],CompositeQ[#]&&AllTrue[FactorInteger[#][[All,1]], PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 08 2018 *)

from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return not isprime(n) and all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(9, 756, 2)))) # Michael S. Branicky, Apr 06 2021

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A046351 Palindromic composite numbers with only palindromic prime factors.

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A046355 Composite numbers with only palindromic prime factors whose sum is palindromic (counted with multiplicity).

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A046350 Odd composite numbers with only palindromic prime factors.

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