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A060792
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Numbers that are palindromic in bases 2 and 3.
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32
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0, 1, 6643, 1422773, 5415589, 90396755477, 381920985378904469, 1922624336133018996235, 2004595370006815987563563, 8022581057533823761829436662099, 392629621582222667733213907054116073, 32456836304775204439912231201966254787, 428027336071597254024922793107218595973
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OFFSET
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1,3
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COMMENTS
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a(18) (if it exists) is greater than 3^93. - Ilya Nikulshin, Feb 22 2016
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LINKS
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EXAMPLE
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6643 is a term: since 6643 = 1100111110011_2 = 100010001_3.
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MATHEMATICA
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pal2Q[n_Integer] := IntegerDigits[n, 2] == Reverse[IntegerDigits[n, 2]]; pal3Q[n_Integer] := IntegerDigits[n, 3] == Reverse[IntegerDigits[n, 3]]; A060792 = {}; Do[If[pal2Q[n] && pal3Q[n], AppendTo[A060792, n]], {n, 12!}]; A060792 (* Vladimir Joseph Stephan Orlovsky, Sep 19 2009 *)
b1=2; b2=3; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 2 10^7}]; lst (* Vincenzo Librandi, Feb 24 2016 *)
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PROG
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(PARI) ispal(n, b)=my(d=digits(n, b)); d==Vecrev(d)
(Python)
from itertools import chain
from gmpy2 import digits, mpz
A060792 = [int(n, 2) for n in chain(map(lambda x:bin(x)[2:]+bin(x)[2:][::-1], range(1, 2**16)), map(lambda x:bin(x)[2:]+bin(x)[2:][-2::-1], range(1, 2**16))) if mpz(int(n, 2)).digits(3) == mpz(int(n, 2)).digits(3)[::-1]] # Chai Wah Wu, Aug 12 2014
(Magma) [n: n in [0..2*10^7] | Intseq(n, 3) eq Reverse(Intseq(n, 3))and Intseq(n, 2) eq Reverse(Intseq(n, 2))]; // Vincenzo Librandi, Feb 24 2016
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CROSSREFS
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KEYWORD
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nonn,base,hard,nice
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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a(7) found by François Boisson, using a Caml program running on an AMD-64 machine. - Bruno Petazzoni, program co-author, Jan 31 2006
a(8) from the same source, May 26 2006
a(9) from Alan Grimes, Dec 16 2013
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STATUS
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approved
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