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A004676 Primes written in base 2. 83
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)
OFFSET
1,1
COMMENTS
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
REFERENCES
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 3.
LINKS
Chris Caldwell, The prime pages, The first 1000 primes.
FORMULA
a(n) = A007088(A000040(n)). - R. J. Mathar, Jun 03 2011
MATHEMATICA
FromDigits /@ IntegerDigits[ Prime[ Range[31]], 2] (* Robert G. Wilson v, Jun 30 2005 *)
PROG
(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
CROSSREFS
Cf. A019434 Fermat primes (base 10), A000668 Mersenne primes (base 10).
Sequence in context: A230297 A086084 A206073 * A303593 A124387 A171796
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved

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Last modified March 19 09:40 EDT 2024. Contains 370981 sequences. (Running on oeis4.)