A319585 Numbers in base 10 that are palindromic in bases 2, 8, and 16.

0, 1, 3, 5, 7, 9, 3951, 4095, 4097, 12291, 20485, 21845, 28679, 30039, 36873, 16187247, 16777215, 16777217, 16781313, 50331651, 50343939, 83886085, 83894277, 83906565, 83914757, 89458005, 89466197, 89478485, 89486677, 117440519, 117448711, 117460999

Offset: 1

Author

Jeremias M. Gomes, Sep 23 2018

Keywords

• nonn
• base

Comments

Intersection of A006995, A029803, and A029730.

Examples

			16187247 = 111101101111111101101111_2 = 75577557_8 = F6FF6F_16.
		

Crossrefs

Cf. A006995 (base 2), A029803 (base 8), and A029730 (base 16).

Programs

Magma

[n: n in [0..2*10^7] | Intseq(n, 2) eq Reverse(Intseq(n, 2)) 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, 2] && 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..10000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]