

A319583


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


0



0, 1, 3, 5, 15, 17, 51, 85, 255, 257, 273, 771, 819, 1285, 1365, 3855, 4095, 4097, 4369, 12291, 13107, 20485, 21845, 61455, 65535, 65537, 65793, 69649, 69905, 196611, 197379, 208947, 209715, 327685, 328965, 348245, 349525, 983055, 986895, 1044735, 1048575
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OFFSET

1,3


COMMENTS

Intersection of A006995, A014192, and A029730.
This sequence is infinite as it contains 15*(1 + 16^k) for any k > 0.  Rémy Sigrist, Sep 23 2018


LINKS

Table of n, a(n) for n=1..41.


EXAMPLE

255 is 11111111 in binary, 3333 in quaternary and FF in hexadecimal. Hence 255 is in the sequence.
Although 21 is 10101 in binary and 111 in quaternary, it is 15 in hexadecimal and therefore not in the sequence.


MATHEMATICA

palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && palQ[n, 4] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* JeanFrançois Alcover, Sep 25 2018 *)


PROG

(Sage) [n for n in (0..1000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(4)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
(MAGMA) [n: n in [0..2*10^7]  Intseq(n, 2) eq Reverse(Intseq(n, 2)) and Intseq(n, 4) eq Reverse(Intseq(n, 4)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018


CROSSREFS

Cf. A006995 (base 2), A014192 (base 4), and A029730 (base 16).
Sequence in context: A192794 A293001 A018358 * A094358 A003527 A004729
Adjacent sequences: A319580 A319581 A319582 * A319584 A319585 A319586


KEYWORD

nonn,base


AUTHOR

Jeremias M. Gomes, Sep 23 2018


STATUS

approved



