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A072762
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n coded as binary word of length=n with k-th bit set iff k is prime (1<=k<=n), decimal value.
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7
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0, 1, 3, 6, 13, 26, 53, 106, 212, 424, 849, 1698, 3397, 6794, 13588, 27176, 54353, 108706, 217413, 434826, 869652, 1739304, 3478609, 6957218, 13914436, 27828872, 55657744, 111315488, 222630977, 445261954, 890523909
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is odd iff n is prime.
a(Prime[n]) = Numerator[ Sum[ 1/2^Prime[k], {k,1,n} ] ]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
The n-th approximation to the Prime Constant is given by a(n)/2^n - Anton Vrba (antonvrba(AT)yahoo.com), Nov 24 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
Eric Weisstein's World of Mathematics, Prime Constant,
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FORMULA
| a(1) = 0 and a(n) = a(n-1)*2 + A010051(n) for n>1.
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EXAMPLE
| a(6)='011010'=(((0*2+1)*2+1)*2*2+1)*2=26; a(7)='0110101'=(((0*2+1)*2+1)*2*2+1)*2*2+1=53; a(8)='01101010'=((((0*2+1)*2+1)*2*2+1)*2*2+1)*2=106.
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MAPLE
| a:= proc(n) option remember;
`if` (n<2, 0, 2 * a(n-1) + `if` (isprime(n), 1, 0))
end:
seq (a(n), n=1..40);
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PROG
| (PARI) an=0; print1(an, ", "); for(n=2, 31, an=2*an+isprime(n); print1(an, ", ")) - W. Bomfim Jan 18, 2011
(Haskell)
a072762 n = foldl (\v d -> 2*v + d) 0 $ map a010051 [1..n]
-- Reinhard Zumkeller, Sep 17 2011
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CROSSREFS
| Cf. A100634, A010051.
Sequence in context: A032198 A079941 A019300 * A081254 A125049 A164991
Adjacent sequences: A072759 A072760 A072761 * A072763 A072764 A072765
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KEYWORD
| nonn,nice,base
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 08 2002
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