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%I #33 Oct 29 2023 16:36:19
%S 0,1,2,3,4,5,6,7,8,9,11,828,858,888,919,949,979,1551,2772,23632,25552,
%T 60106,67576,465564,477774,489984,515515,527725,17577571,26144162,
%U 28300382,39399393,47999974,69455496,2118008112,8050880508
%N Numbers that are palindromic in bases 10 and 15.
%H Robert G. Wilson v, <a href="/A029970/b029970.txt">Table of n, a(n) for n = 1..72</a> (first 69 terms from Ray Chandler)
%H P. De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>
%t NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]] ]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]] ]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[idfhn]], Mod[l, 2]] ]]] ]]]; palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 15], AppendTo[l, a]], {n, 200000}]; l (* _Robert G. Wilson v_, Sep 03 2004 *)
%t b1=10; b2=15; 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, 10^5], PalindromeQ[#] && # == IntegerReverse[#, 15] &] (* _Robert Price_, Nov 09 2019 *)
%o (Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 15) eq Reverse(Intseq(n, 15))]; // _Vincenzo Librandi_, Nov 23 2014
%Y Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029731, A097855, A099165.
%K nonn,base
%O 1,3
%A _Patrick De Geest_
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