%I #17 Sep 08 2022 08:46:23
%S 0,1,2,3,5,170,4095,4097,8194,12291,20485,21845,696490,699050,
%T 16777215,16777217,16781313,16785409,16789505,33554434,33558530,
%U 33562626,33566722,50331651,50335747,50339843,50343939,83886085,83906565,89458005,89478485
%N Numbers in base 10 that are palindromic in bases 4, 8 and 16.
%e 170 = 2222_4 = 252_8 = AA_16. Hence 170 is in the sequence.
%t palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
%t Reap[Do[If[palQ[n, 4] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* _Jean-François Alcover_, Sep 25 2018 *)
%o (Sage) [n for n in (0..100000) if Word(n.digits(4)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
%o (Magma) [n: n in [0..2*10^7] | Intseq(n, 4) eq Reverse(Intseq(n, 4)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // _Vincenzo Librandi_, Sep 24 2018
%Y Intersection of A014192, A029803 and A029730.
%K nonn,base
%O 1,3
%A _Jeremias M. Gomes_, Sep 24 2018
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