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A011592
Legendre symbol (n,47).
31
0, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1
OFFSET
0,1
COMMENTS
From Jianing Song, Dec 13 2025: (Start)
The Dirichlet character associated with the imaginary quadratic field Q(sqrt(-47)).
Note that (Sum_{i=0..46} i*a(i))/(-47) = 5 gives the class number of the imaginary quadratic field Q(sqrt(-47)). (End)
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 68.
LINKS
Eric Weisstein's World of Mathematics, Class Number.
Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1).
FORMULA
From Jianing Song, Dec 13 2025: (Start)
a(n) = (Prod_{1<=k<=23} sin(2*k*Pi/47))/(Prod_{1<=k<=23} sin(2*Pi/47)) = (sqrt(47)/2^23) * (Prod_{1<=k<=23} sin(2*k*Pi/47)).
Sum_{n>=1} a(n)/n = -(Pi/47^(3/2)) * (Sum_{i=0..46} i*a(i)) = 5*Pi/sqrt(47) (Dirichlet class number formula). (End)
MATHEMATICA
JacobiSymbol[Range[0, 100], 47] (* Paolo Xausa, Nov 08 2025 *)
CROSSREFS
Moebius transform of A035143.
Cf. A191033 (primes decomposing in Q(sqrt(-47))), A191072 (primes remaining inert).
Kronecker symbols {(D/n)} for negative fundamental discriminants D = -3..-47, -67, -163: A102283, A101455, A175629, A188510, A011582, A316569, A011585, A289741, A011586, A109017, A011588, A390614, A388073, A388072, A011591, this sequence, A011596, A011615.
Kronecker symbols {(D/n)} for positive fundamental discriminants D = 5..41: A080891, A091337, A110161, A011583, A011584, A322829, A322796, A390615, A011587, A391502, A011589, A391503, A011590.
Sequence in context: A011589 A011590 A011591 * A011593 A011594 A011595
KEYWORD
sign,mult,easy
STATUS
approved