A095103 4k+3 primes whose Legendre-vector is not valid Dyck-path.

19, 43, 67, 107, 127, 139, 163, 179, 211, 223, 227, 283, 307, 331, 347, 367, 379, 443, 463, 467, 487, 491, 499, 523, 547, 571, 587, 619, 631, 643, 683, 691, 727, 739, 787, 811, 823, 827, 859, 883, 907, 947, 967, 1019, 1051, 1087, 1123, 1163

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn

Links

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

Crossrefs

Intersection of A000040 and A095101. Complement of A095102 in A002145.

Cf. A095093, A095108 (diving indices).

Programs

Mathematica

L = {}; Do[p = Prime[k]; If[Mod[p, 4] == 3 && Min[Table[Sum[JacobiSymbol[n, p], {n, 0, m}], {m, 0, p - 1}]] < 0, L = Append[L, p]], {k, 1, 192}]; L (* From Jonathan Sondow, Oct 25 2011 *)

PARI

isok(m) = {my(s=0); if(m%4==3&&isprime(m), for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; } \\ Jinyuan Wang, Jul 20 2020

Sage

def A095103_list(n) :
    def is_Motzkin(n, k):
        s = 0
        for i in (1..k) :
            s += jacobi_symbol(i, n)
            if s < 0 : return false
        return true
    P = filter(is_prime, range(n+1)[3::4])
    return filter(lambda m: not is_Motzkin(m, m//2), P)
A095103_list(1163) # Peter Luschny, Aug 08 2012

Formula

a(n) = 4*A095273(n) + 3.