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A166405
Sum of those positive i <= 2n+1, for which J(i,2n+1)=-1. Here J(i,k) is the Jacobi symbol.
3
0, 2, 5, 14, 0, 33, 39, 45, 68, 95, 63, 161, 0, 126, 203, 279, 165, 245, 333, 312, 410, 473, 270, 658, 0, 459, 689, 660, 513, 944, 915, 630, 780, 1139, 759, 1491, 1314, 775, 1155, 1738, 0, 1826, 1360, 1479, 1958, 1729, 1395, 2090, 2328, 1485, 2525, 2884
OFFSET
0,2
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) obtaining value -1 when i=2, 6, 7, 8 and 10, thus a(5)=33.
MATHEMATICA
Table[Total@ Select[Range[2n + 1], JacobiSymbol[#, 2n + 1]==-1 &], {n, 0, 100}] (* Indranil Ghosh, Jun 12 2017 *)
PROG
(MIT/GNU Scheme)
(define (A166405 n) (let ((w (A005408 n))) (let loop ((i 1) (s 0)) (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
A125615(n)=a(A102781(n)). Cf. A166100, A166406-A166408. The cases where a(i)/A005408(i) is not integer seem also to be given by A166101. This is NOT a bisection of A165898. Scheme-code for jacobi-symbol is given at A165601.
Sequence in context: A272106 A190478 A155838 * A226505 A370235 A279176
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 21 2009
STATUS
approved