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Search: id:A072762
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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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+0
5
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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; listen)
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OFFSET
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1,3
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COMMENT
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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
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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
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a(1) = 0 and a(n) = a(n-1)*2 + A010051(n) for n>1.
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EXAMPLE
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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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CROSSREFS
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Adjacent sequences: A072759 A072760 A072761 this_sequence A072763 A072764 A072765
Sequence in context: A032198 A079941 A019300 this_sequence A081254 A125049 A123247
Cf. A100634
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KEYWORD
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nonn,nice
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 08 2002
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