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

1,3

Links

Table of n, a(n) for n=1..31.

Example

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

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 *)

Prog

(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()]
(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

Crossrefs

Intersection of A014192, A029803 and A029730.

Sequence in context: A160600 A325505 A366642 * A140551 A064936 A041655

Adjacent sequences: A319606 A319607 A319608 * A319610 A319611 A319612

Keyword

nonn,base

Author

Jeremias M. Gomes, Sep 24 2018

Status

approved