A217054 - OEIS

%I #13 Jan 21 2016 11:16:24

%S 9,2,8,3,1,9,5,9,1,2,5,9,9,4,0,4,1,6,0,6,8,9,1,0,8,6,7,3,1,8,4,7,3,3,

%T 0,6,8,2,9,1,3,0,6,7,6,5,6,1,0,5,5,3,6,9,7,5,7,1,1,2,3,2,9,8,4,7,4,6,

%U 3,2,5,8,3,8,2,8,3,2,2,1,3,3,5,6,2,9,8,4,1,2,6,9,7,2,5,6,1

%N Odd number version of the prime constant (A101264 interpreted as a binary number).

%C The prime constant (A051006) is essentially a set of flags that tell us whether a given integer is prime. But since all even numbers (except 2) are composite, every other bit is guaranteed to be 0.

%C Depending on the algorithm for which this is used, it may be more efficient to store a set of flags for just the odd numbers (and handle 2 as a special case). Lehmer (1969) suggests using about 64 kilobytes for the storage of this "characteristic number."

%D D. H. Lehmer, "Computer Technology Applied to the Theory of Numbers," from Studies in Number Theory, ed. William J. LeVeque. Englewood Cliffs, New Jersey: Prentice Hall (1969): 138.

%F sum(k = 1 .. infinity, chi(2k + 1)/2^k), where chi(n) is the characteristic function of the prime numbers (A010051).

%F sum(k = 2 .. infinity, 1/2^((p(k) - 1)/2)), where p(k) is the k-th prime number.

%e 1/2 + 1/4 + 1/8 + 1/32 + 1/64 + ... = 0.928319591...

%t RealDigits[Sum[1/2^((Prime[k] - 1)/2), {k, 2, 1000}], 10, 100][[1]]

%o (PARI) s=0; forprime(p=3, default(realprecision)*log(100)\log(2)+9, s += 1.>>(p\2)); s \\ _Charles R Greathouse IV_, Sep 26 2012

%K nonn,cons

%O 0,1

%A _Alonso del Arte_, Sep 25 2012