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A004676
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Primes written in base 2.
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80
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10, 11, 101, 111, 1011, 1101, 10001, 10011, 10111, 11101, 11111, 100101, 101001, 101011, 101111, 110101, 111011, 111101, 1000011, 1000111, 1001001, 1001111, 1010011, 1011001, 1100001, 1100101, 1100111, 1101011, 1101101, 1110001, 1111111, 10000011, 10001001
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The only primes of binary weight 2 are the Fermat primes (only five are known: 11, 101, 10001, 100000001, 10000000000000001); the repunits base 2 are the Mersenne primes. - Daniel Forgues, Nov 07 2011
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 3.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Chris Caldwell, The prime pages, The first 1000 primes.
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FORMULA
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a(n) = A007088(A000040(n)). - R. J. Mathar, Jun 03 2011
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MATHEMATICA
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FromDigits /@ IntegerDigits[ Prime[ Range[31]], 2] (* Robert G. Wilson v, Jun 30 2005 *)
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PROG
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(Haskell)
a004676 = a007088 . a000040 -- Reinhard Zumkeller, Aug 06 2012
(PARI) a(n)=subst(Pol(binary(prime(n))), 'x, 10) \\ Charles R Greathouse IV, Mar 20 2013
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CROSSREFS
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Cf. A019434 Fermat primes (base 10), A000668 Mersenne primes (base 10).
Cf. A174332, A208238, A208241.
Sequence in context: A230297 A086084 A206073 * A303593 A124387 A171796
Adjacent sequences: A004673 A004674 A004675 * A004677 A004678 A004679
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KEYWORD
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nonn,easy,base
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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