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%I #24 Sep 08 2022 08:46:13
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U 49,50,51,52,53,54,55,56,57,58,59,61,122,183,244,305,366
%N Numbers that are palindromes in base-60 representation.
%H Reinhard Zumkeller, <a href="/A262065/b262065.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Palindromic_number">Palindromic number</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>
%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e . n | a(n) | base 60 n | a(n) | base 60
%e . -----+------+----------- ------+-------+--------------
%e . 100 | 2440 | [40, 40] 1000 | 56355 | [15, 39, 15]
%e . 101 | 2501 | [41, 41] 1001 | 56415 | [15, 40, 15]
%e . 102 | 2562 | [42, 42] 1002 | 56475 | [15, 41, 15]
%e . 103 | 2623 | [43, 43] 1003 | 56535 | [15, 42, 15]
%e . 104 | 2684 | [44, 44] 1004 | 56595 | [15, 43, 15]
%e . 105 | 2745 | [45, 45] 1005 | 56655 | [15, 44, 15]
%e . 106 | 2806 | [46, 46] 1006 | 56715 | [15, 45, 15]
%e . 107 | 2867 | [47, 47] 1007 | 56775 | [15, 46, 15]
%e . 108 | 2928 | [48, 48] 1008 | 56835 | [15, 47, 15]
%e . 109 | 2989 | [49, 49] 1009 | 56895 | [15, 48, 15]
%e . 110 | 3050 | [50, 50] 1010 | 56955 | [15, 49, 15]
%e . 111 | 3111 | [51, 51] 1011 | 57015 | [15, 50, 15]
%e . 112 | 3172 | [52, 52] 1012 | 57075 | [15, 51, 15]
%e . 113 | 3233 | [53, 53] 1013 | 57135 | [15, 52, 15]
%e . 114 | 3294 | [54, 54] 1014 | 57195 | [15, 53, 15]
%e . 115 | 3355 | [55, 55] 1015 | 57255 | [15, 54, 15]
%e . 116 | 3416 | [56, 56] 1016 | 57315 | [15, 55, 15]
%e . 117 | 3477 | [57, 57] 1017 | 57375 | [15, 56, 15]
%e . 118 | 3538 | [58, 58] 1018 | 57435 | [15, 57, 15]
%e . 119 | 3599 | [59, 59] 1019 | 57495 | [15, 58, 15]
%e . 120 | 3601 | [1, 0, 1] 1020 | 57555 | [15, 59, 15]
%e . 121 | 3660 | [1, 1, 0] 1021 | 57616 | [16, 0, 16]
%e . 122 | 3661 | [1, 1, 1] 1022 | 57676 | [16, 1, 16]
%e . 123 | 3721 | [1, 2, 1] 1023 | 57736 | [16, 2, 16]
%e . 124 | 3781 | [1, 3, 1] 1024 | 57796 | [16, 3, 16]
%e . 125 | 3841 | [1, 4, 1] 1025 | 57856 | [16, 4, 16] .
%t f[n_, b_]:=Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 60], AppendTo[lst, n]], {n, 400}]; lst (* _Vincenzo Librandi_, Aug 24 2016 *)
%t pal60Q[n_]:=Module[{idn60=IntegerDigits[n,60]},idn60==Reverse[idn60]]; Select[Range[0,400],pal60Q] (* _Harvey P. Dale_, Nov 04 2017 *)
%o (Haskell)
%o import Data.List.Ordered (union)
%o a262065 n = a262065_list !! (n-1)
%o a262065_list = union us vs where
%o us = [val60 $ bs ++ reverse bs | bs <- bss]
%o vs = [0..59] ++ [val60 $ bs ++ cs ++ reverse bs |
%o bs <- tail bss, cs <- take 60 bss]
%o bss = iterate s [0] where
%o s [] = [1]; s (59:ds) = 0 : s ds; s (d:ds) = (d + 1) : ds
%o val60 = foldr (\b v -> 60 * v + b) 0
%o (Magma) [n: n in [0..600] | Intseq(n, 60) eq Reverse(Intseq(n, 60))]; // _Vincenzo Librandi_, Aug 24 2016
%o (PARI) isok(m) = my(d=digits(m, 60)); d == Vecrev(d); \\ _Michel Marcus_, Jan 22 2022
%Y Cf. A262079 (first differences).
%Y Intersection with A002113: A262069.
%Y Corresponding sequences for bases 2 through 12: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113, A029956, A029957.
%K nonn,base,look
%O 1,3
%A _Reinhard Zumkeller_, Sep 10 2015
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