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A319585
Numbers in base 10 that are palindromic in bases 2, 8, and 16.
0
0, 1, 3, 5, 7, 9, 3951, 4095, 4097, 12291, 20485, 21845, 28679, 30039, 36873, 16187247, 16777215, 16777217, 16781313, 50331651, 50343939, 83886085, 83894277, 83906565, 83914757, 89458005, 89466197, 89478485, 89486677, 117440519, 117448711, 117460999
OFFSET
1,3
COMMENTS
Intersection of A006995, A029803, and A029730.
EXAMPLE
16187247 = 111101101111111101101111_2 = 75577557_8 = F6FF6F_16.
MATHEMATICA
palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
Reap[Do[If[palQ[n, 2] && 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..10000) if Word(n.digits(2)).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, 2) eq Reverse(Intseq(n, 2)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
CROSSREFS
Cf. A006995 (base 2), A029803 (base 8), and A029730 (base 16).
Sequence in context: A316492 A062887 A062886 * A133452 A356665 A251364
KEYWORD
nonn,base
AUTHOR
Jeremias M. Gomes, Sep 23 2018
STATUS
approved