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

1,1

Comments

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

Links

Table of n, a(n) for n=1..50.

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

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

Adjacent sequences: A095098 A095099 A095100 * A095102 A095103 A095104

Keyword

nonn

Author

Antti Karttunen and Jun 01 2004

Status

approved