A319609 Numbers in base 10 that are palindromic in bases 4, 8 and 16.

0, 1, 2, 3, 5, 170, 4095, 4097, 8194, 12291, 20485, 21845, 696490, 699050, 16777215, 16777217, 16781313, 16785409, 16789505, 33554434, 33558530, 33562626, 33566722, 50331651, 50335747, 50339843, 50343939, 83886085, 83906565, 89458005, 89478485

Offset: 1

Author

Jeremias M. Gomes, Sep 24 2018

Keywords

• nonn
• base

Examples

			170 = 2222_4 = 252_8 = AA_16. Hence 170 is in the sequence.
		

Crossrefs

Intersection of A014192, A029803 and A029730.

Programs

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

Mathematica

palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
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 *)

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()]