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A262069 Palindromes in base 10 that are also palindromes in base 60.

%I A262069 #25 Feb 16 2025 08:33:27
%S A262069 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,55155,55455,55755,57075,57375,
%T A262069 113311,148841,2796972,8372738,11166111,14033041,26233262,28933982,
%U A262069 150050051,151141151,152070251,152232251,153161351,153323351,154252451,154414451,155343551,155505551
%N A262069 Palindromes in base 10 that are also palindromes in base 60.
%H A262069 Chai Wah Wu, <a href="/A262069/b262069.txt">Table of n, a(n) for n = 1..82</a>
%H A262069 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H A262069 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>
%H A262069 Wikipedia, <a href="http://www.wikipedia.org/wiki/Palindromic_number">Palindromic number</a>
%H A262069 Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>
%H A262069 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e A262069 n = 22: 41*60^2 + 20*60^1 + 41*60^0 = A262065(2541) = A002113(1148) = 148841 = a(22);
%e A262069 n = 27: 2*60^4 + 1*60^3 + 27*60^2 + 1*60^1 + 2*60^0 = A262065(7348) = A002113(12623) = 26233262 = a(27).
%t A262069 palQ[n_Integer, base_Integer]:=Module[{idn=IntegerDigits[n, base]}, idn==Reverse[idn]]; Select[Range[10^6], palQ[#, 10]&& palQ[#, 60] &] (* _Vincenzo Librandi_, Sep 11 2015 *)
%o A262069 (Haskell)
%o A262069 -- import Data.List.Ordered (isect)
%o A262069 a262069 n = a262069_list !! (n-1)
%o A262069 a262069_list = isect a002113_list a262065_list
%o A262069 (Python)
%o A262069 def palgen(l,b=10): # generator of palindromes in base b of length <= 2*l
%o A262069     if l > 0:
%o A262069         yield 0
%o A262069         for x in range(1,l+1):
%o A262069             n = b**(x-1)
%o A262069             n2 = n*b
%o A262069             for y in range(n,n2):
%o A262069                 k, m = y//b, 0
%o A262069                 while k >= b:
%o A262069                     k, r = divmod(k,b)
%o A262069                     m = b*m + r
%o A262069                 yield y*n + b*m + k
%o A262069             for y in range(n,n2):
%o A262069                 k, m = y, 0
%o A262069                 while k >= b:
%o A262069                     k, r = divmod(k,b)
%o A262069                     m = b*m + r
%o A262069                 yield y*n2 + b*m + k
%o A262069 A262069_list = [n for n in palgen(5,60) if str(n) == str(n)[::-1]] # _Chai Wah Wu_, Sep 10 2015
%o A262069 (Magma) [n: n in [0..2*10^7] | Intseq(n, 60) eq Reverse(Intseq(n, 60)) and Intseq(n, 10) eq Reverse(Intseq(n, 10))]; // _Vincenzo Librandi_, Sep 11 2015
%o A262069 (PARI) ispal(v) = v == Vecrev(v);
%o A262069 isok(n) = ispal(digits(n)) && ispal(digits(n,60)); \\ _Michel Marcus_, Sep 11 2015
%Y A262069 Intersection of A002113 and A262065.
%K A262069 nonn,base
%O A262069 1,3
%A A262069 _Reinhard Zumkeller_, Sep 10 2015
%E A262069 More terms from _Chai Wah Wu_, Sep 10 2015