A319598 - OEIS

%I #32 Jun 24 2019 16:47:43

%S 0,1,3,5,4095,4097,12291,20485,21845,16777215,16777217,16781313,

%T 50331651,50343939,83886085,83906565,89458005,89478485,68702703615,

%U 68719476735,68719476737,68736258049,206158430211,206208774147,343597383685,343602954245,343681290245

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

%C Intersection of A006995, A014192, A029803, and A029730.

%C 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

%H A.H.M. Smeets, <a href="/A319598/b319598.txt">Table of n, a(n) for n = 1..114</a> (first 70 terms from Rémy Sigrist)

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

%t palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];

%t 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 *)

%o (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()]

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

%K nonn,base

%O 1,3

%A _Jeremias M. Gomes_, Sep 24 2018

%E a(19)-a(27) from _Rémy Sigrist_, Nov 15 2018