A319598 Numbers in base 10 that are palindromic in bases 2, 4, 8, and 16.

0, 1, 3, 5, 4095, 4097, 12291, 20485, 21845, 16777215, 16777217, 16781313, 50331651, 50343939, 83886085, 83906565, 89458005, 89478485, 68702703615, 68719476735, 68719476737, 68736258049, 206158430211, 206208774147, 343597383685, 343602954245, 343681290245

Offset: 1

Author

Jeremias M. Gomes, Sep 24 2018

Keywords

• nonn
• base

Comments

Intersection of A006995, A014192, A029803, and A029730.

This sequence is infinite because it contains terms of the forms 4096^k-1 (k>=0) and 4096^k+1 (k>0). - Bruno Berselli, Sep 24 2018

Examples

			4095 = 111111111111_2 = 333333_4 = 7777_8 = FFF_16. Hence 4095 is in the sequence.
		

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..114 (first 70 terms from Rémy Sigrist)

Crossrefs

Cf. A006995 (base 2), A014192 (base 4), A029803 (base 8), and A029730 (base 16).

Programs

Mathematica

palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && 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(2)).is_palindrome() and Word(n.digits(4)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]

Extensions

a(19)-a(27) from Rémy Sigrist, Nov 15 2018