A085108 Decimal expansion of sum 1/(p*2^p) where p runs through the set of Artin primes (primes with primitive root 2).

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

Offset

0,2

Comments

David H. Bailey and Richard E. Crandal conjectured that this constant is 2-normal.

References

David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, 2000

Links

Table of n, a(n) for n=0..103.

Formula

c=0.0479705463464....

Mathematica

Join[{0}, RealDigits[Total[1/(# 2^#)&/@Select[Prime[Range[100]], PrimitiveRoot[ #, 2]==2&]], 10, 120][[1]]] (* Harvey P. Dale, Apr 02 2018 *)

Prog

(PARI) sum(k=1, 2000, if(znprimroot(prime(k))-2, 0, 1)*1./prime(k)/2^prime(k))

Crossrefs

Cf. A001122, A085114.

Sequence in context: A371525 A105169 A200618 * A106502 A046254 A268227

Adjacent sequences: A085105 A085106 A085107 * A085109 A085110 A085111

Keyword

cons,nonn

Author

Benoit Cloitre, Aug 10 2003

Status

approved