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A166100
Sum of those positive i <= 2n+1, for which J(i,2n+1)=+1. Here J(i,k) is the Jacobi symbol.
6
1, 1, 5, 7, 27, 22, 39, 15, 68, 76, 63, 92, 250, 117, 203, 186, 165, 175, 333, 156, 410, 430, 270, 423, 1029, 357, 689, 440, 513, 767, 915, 504, 780, 1072, 759, 994, 1314, 725, 1155, 1343, 2187, 1577, 1360, 957, 1958, 1547, 1395, 1330, 2328, 1485, 2525
OFFSET
0,3
COMMENTS
Note that this sequence is not equal to the sum of the quadratic residues of 2n+1 in range [1,2n+1], and thus NOT a bisection of A165898.
LINKS
EXAMPLE
For n=5, we get odd number 11 (2*5+1), and J(i,11) = 1,-1,1,1,1,-1,-1,-1,1,-1,0 when i ranges from 1 to 11, J(i,11) getting value 1 when i=1, 3, 4, 5 and 9, thus a(5)=22.
MATHEMATICA
Table[Total[Flatten[Position[JacobiSymbol[Range[2n+1], 2n+1], 1]]], {n, 0, 50}] (* Harvey P. Dale, Jun 19 2013 *)
PROG
(MIT Scheme:) (define (A166100 n) (let ((w (A005408 n))) (let loop ((i 1) (s 1)) (cond ((= i w) s) (else (loop (1+ i) (+ s (if (= 1 (jacobi-symbol (1+ i) w)) (1+ i) 0))))))))
(Python)
from sympy import jacobi_symbol as J
def a(n): return sum([i for i in range(1, 2*n + 2) if J(i, 2*n + 1)==1]) # Indranil Ghosh, Jun 12 2017
CROSSREFS
Scheme-code for jacobi-symbol is given at A165601.
Sequence in context: A067701 A059240 A324363 * A135606 A051845 A278646
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 13 2009. Erroneous name corrected Oct 20 2009.
STATUS
approved