login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072762 n coded as binary word of length=n with k-th bit set iff k is prime (1<=k<=n), decimal value. 9
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 (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.

a(n) = (1/2)*(pi(n) + Sum_{i=1..n} 2^(n-i)*pi(i)), where pi = A000720. - Ridouane Oudra, Aug 26 2019

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);  #  Alois P. Heinz, Jan 18 2011

MATHEMATICA

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 *)

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, A000720, A118255.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 23:45 EDT 2020. Contains 334581 sequences. (Running on oeis4.)