cp's OEIS Frontend

A035132 Nonsquarefree palindromes.

%I A035132 #30 Feb 16 2025 08:32:37
%S A035132 4,8,9,44,88,99,121,171,212,232,242,252,272,292,333,343,363,404,414,
%T A035132 424,444,464,484,525,575,585,616,636,656,666,676,686,696,747,808,828,
%U A035132 848,868,888,909,999,1331,1881,2112,2332,2552,2662,2772,2992,3663,3773
%N A035132 Nonsquarefree palindromes.
%H A035132 Amiram Eldar, <a href="/A035132/b035132.txt">Table of n, a(n) for n = 1..10000</a>
%H A035132 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%e A035132 4114 = 2 * 11^2 * 17.
%t A035132 sfQ[n_]:=Max[Transpose[FactorInteger[n]][[2]]]>1; palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; Select[Range[2,3776],sfQ[#] && palQ[#] &] (* _Jayanta Basu_, May 12 2013 *)
%t A035132 Select[Range[4000], PalindromeQ[#] && !SquareFreeQ[#] &] (* _Amiram Eldar_, Feb 25 2021 *)
%o A035132 (Python)
%o A035132 from itertools import product
%o A035132 from sympy.ntheory.factor_ import core
%o A035132 def palsthru(maxdigits):
%o A035132   midrange = [[""], [str(i) for i in range(10)]]
%o A035132   for digits in range(1, maxdigits+1):
%o A035132     for p in product("0123456789", repeat=digits//2):
%o A035132       left = "".join(p)
%o A035132       if len(left) and left[0] == '0': continue
%o A035132       for middle in midrange[digits%2]: yield int(left+middle+left[::-1])
%o A035132 def okpal(p): return p > 3 and core(p, 2) != p
%o A035132 print(list(filter(okpal, palsthru(4)))) # _Michael S. Branicky_, Apr 08 2021
%Y A035132 Intersection of A002113 and A013929.
%Y A035132 Supersequence of A077572.
%Y A035132 Cf. A005117, A035133, A071251, A075804 (first differences).
%K A035132 nonn,base
%O A035132 1,1
%A A035132 _Patrick De Geest_, Nov 15 1998