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.

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

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn

Comments

Integers whose Jacobi-vector does not form a valid Motzkin-path.

Links

• Antti Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Subset of A095103. Complement of A095100 in A004767.

Cf. A095091.

Programs

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

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

Formula

a(n) = 4*A095275(n) + 3.