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A072762 n coded as binary word of length=n with k-th bit set iff k is prime (1<=k<=n), decimal value. 7
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; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..300

Eric Weisstein's World of Mathematics, Prime Constant.

FORMULA

a(1) = 0 and a(n) = a(n-1)*2 + A010051(n) for n>1.

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.

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);

MATHEMATICA

a[1] = 0; a[n_] := a[n] = 2*a[n-1] + Boole[PrimeQ[n]]; Table[a[n], {n, 1, 31}] (* Jean-Fran├žois 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 *)

PROG

(PARI) an=0; print1(an, ", "); for(n=2, 31, an=2*an+isprime(n); print1(an, ", ")) \\ Washington Bomfim, Jan 18 2011

(PARI) a(n)=my(s=1, p=2); forprime(q=3, n, s=s<<(q-p)+1; p=q); s<<(n-p) \\ Charles R Greathouse IV, Jun 03 2013

(Haskell)

a072762 n = foldl (\v d -> 2*v + d) 0 $ map a010051 [1..n]

-- Reinhard Zumkeller, Sep 17 2011

CROSSREFS

Cf. A100634, A010051.

Sequence in context: A267367 A265385 A019300 * A081254 A125049 A267581

Adjacent sequences:  A072759 A072760 A072761 * A072763 A072764 A072765

KEYWORD

nonn,nice,base

AUTHOR

Reinhard Zumkeller, Aug 08 2002

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.