login
A271547
Decimal expansion of Product_{p prime} (1+1/(2p))*sqrt(1-1/p), a constant related to the asymptotic average number of squares modulo n.
2
8, 1, 2, 1, 0, 5, 7, 1, 1, 1, 6, 3, 1, 2, 2, 5, 1, 1, 7, 0, 6, 2, 5, 0, 9, 6, 4, 5, 8, 1, 8, 8, 7, 1, 7, 6, 5, 6, 0, 5, 7, 7, 1, 0, 0, 4, 8, 3, 6, 6, 9, 9, 2, 4, 3, 6, 0, 9, 2, 1, 8, 2, 0, 0, 3, 7, 8, 0, 9, 4, 0, 6, 2, 0, 4, 2, 5, 3, 2, 2, 0, 7, 5, 5, 8, 0, 2, 5, 4, 0, 2, 3, 5, 0, 4, 0, 2, 9, 9, 8
OFFSET
0,1
LINKS
Steven R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.
FORMULA
Equals exp(Sum_{n>=2} -( (-1)^n + 2^(n-1))*P(n)/(n*2^n), where P(n) is the prime zeta P function.
EXAMPLE
0.81210571116312251170625096458188717656057710048366992436092182...
MATHEMATICA
digits = 100; Exp[NSum[-( (-1)^n + 2^(n - 1))*PrimeZetaP[n]/(n* 2^n), {n, 2, Infinity}, NSumTerms -> 3 digits, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
CROSSREFS
Sequence in context: A198830 A254244 A232068 * A010154 A109011 A225767
KEYWORD
nonn,cons
AUTHOR
STATUS
approved