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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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9
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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, 1781047818, 3562095636, 7124191272
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OFFSET
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1,3
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COMMENTS
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a(n) is odd iff n is prime.
a(p) where p is prime is the numerator of Sum_{q <= p} 1/2^q where the sum is over primes up to p. - Alexander Adamchuk, 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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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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MAPLE
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a:= proc(n) option remember;
`if`(n<2, 0, 2 * a(n-1) + `if`(isprime(n), 1, 0))
end:
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MATHEMATICA
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a[1] = 0; a[n_] := a[n] = 2*a[n-1] + Boole[PrimeQ[n]]; Table[a[n], {n, 1, 31}] (* Jean-François Alcover, Jun 14 2013 *)
nxt[{n_, a_}]:={n+1, Boole[PrimeQ[n+1]]+2a}; Transpose[NestList[nxt, {1, 0}, 30]][[2]] (* Harvey P. Dale, Jan 07 2015 *)
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PROG
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(PARI) an=0; print1(an, ", "); for(n=2, 31, an=2*an+isprime(n); print1(an, ", ")) \\ Washington Bomfim, Jan 18 2011
(Haskell)
a072762 n = foldl (\v d -> 2*v + d) 0 $ map a010051 [1..n]
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CROSSREFS
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KEYWORD
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nonn,nice,base
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AUTHOR
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STATUS
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approved
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