A217054 Odd number version of the prime constant (A101264 interpreted as a binary number).

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, 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, 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

Offset

0,1

Comments

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.

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."

References

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.

Links

Table of n, a(n) for n=0..96.

Formula

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A248316 A019733 A111722 * A298514 A343215 A137301

Adjacent sequences: A217051 A217052 A217053 * A217055 A217056 A217057

Keyword

nonn,cons

Author

Alonso del Arte, Sep 25 2012

Status

approved