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

1,3

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

Links

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

Example

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

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 *)

Prog

(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()]

Crossrefs

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

Sequence in context: A364551 A138154 A333269 * A353135 A126334 A068635

Adjacent sequences: A319595 A319596 A319597 * A319599 A319600 A319601

Keyword

nonn,base

Author

Jeremias M. Gomes, Sep 24 2018

Extensions

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

Status

approved