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A095101
Integers m of the form 4k+3 for which some of the sums Sum_{i=1..u} J(i/m) (with u ranging from 1 to (m-1)) is negative, where J(i/m) is Jacobi symbol of i and m.
6
19, 43, 51, 67, 91, 99, 107, 115, 123, 127, 139, 147, 155, 163, 179, 187, 195, 203, 207, 211, 219, 223, 227, 235, 247, 259, 267, 275, 283, 291, 307, 315, 323, 331, 339, 347, 355, 367, 379, 387, 403, 411, 423, 427, 435, 443, 451, 459, 463, 467
OFFSET
1,1
COMMENTS
Integers whose Jacobi-vector does not form a valid Motzkin-path.
FORMULA
a(n) = 4*A095275(n) + 3.
PROG
(Sage)
def is_Motzkin(n, k):
s = 0
for i in (1..k) :
s += jacobi_symbol(i, n)
if s < 0 : return False
return True
def A095101_list(n):
return [m for m in range(3, n+1, 4) if not is_Motzkin(m, m//2)]
A095101_list(467) # Peter Luschny, Aug 08 2012
(PARI) isok(m) = {my(s=0); if(m%4==3, for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; } \\ Jinyuan Wang, Jul 20 2020
CROSSREFS
Subset of A095103. Complement of A095100 in A004767.
Cf. A095091.
Sequence in context: A001986 A270123 A139811 * A162856 A095086 A095079
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 01 2004
STATUS
approved