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%I #13 Mar 17 2023 10:29:14
%S 0,1,2,3,4,5,6,7,8,9,11,22,525,575,2332,4664,6226,6996,8558,10001,
%T 11011,12621,13631,374473,1851581,2207022,2267622,2762672,3118113,
%U 3673763,4029204,4296924,4925294,5103015,5836385,6014106,6281826,6747476,7132317,7192917,7658567,7865687
%N Palindromic in bases 10 and 24.
%H Robert G. Wilson v, <a href="/A250409/b250409.txt">Table of n, a(n) for n = 1..99</a>
%t palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; genPal[n_] := Block[{id = IntegerDigits@ n, insert = {{}, {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}}, FromDigits@ Join[id, #, Reverse@ id] & /@ insert]; k = 1; lst = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; While[k < 1000001, s = Select[ genPal[k], palQ[#, 24] &]; If[s != {}, AppendTo[lst, s]; Print@ s; lst = Sort@ Flatten@ lst]; k++]; lst
%t b1=10; b2=24; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* _Vincenzo Librandi_, Nov 23 2014 *)
%t Select[Range[0,79*10^5],PalindromeQ[#]&&IntegerDigits[#,24]== Reverse[ IntegerDigits[ #,24]]&] (* _Harvey P. Dale_, Mar 17 2023 *)
%o (Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 24) eq Reverse(Intseq(n, 24))]; // _Vincenzo Librandi_, Nov 23 2014
%Y Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250410, A250411, A099165, A250412.
%K nonn,base
%O 1,3
%A _Robert G. Wilson v_, Nov 22 2014
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