A095100 Integers m of the form 4k+3 for which all sums Sum_{i=1..u} J(i/m) (with u ranging from 1 to (m-1)) are nonnegative, where J(i/m) is Jacobi symbol of i and m.

3, 7, 11, 15, 23, 27, 31, 35, 39, 47, 55, 59, 63, 71, 75, 79, 83, 87, 95, 103, 111, 119, 131, 135, 143, 151, 159, 167, 171, 175, 183, 191, 199, 215, 231, 239, 243, 251, 255, 263, 271, 279, 287, 295, 299, 303, 311, 319, 327, 335, 343, 351, 359, 363

Offset

1,1

Comments

Integers whose Jacobi-vector forms a valid Motzkin-path.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 4*A095274(n) + 3.

Mathematica

isMotzkin[n_, k_] := Module[{s = 0, r = True}, Do[s += JacobiSymbol[i, n]; If[s < 0, r = False; Break[]], {i, 1, k}]; r]; A095100[n_] := Select[4*Range[0, n+1]+3, isMotzkin[#, Quotient[#, 2]] &]; A095100[90] (* Jean-François Alcover, Oct 08 2013, translated from Sage *)

Prog

(Sage)
def is_Motzkin(n, k):
    s = 0
    for i in range(1, k + 1) :
        s += jacobi_symbol(i, n)
        if s < 0: return False
    return True
def A095100_list(n):
    return [m for m in range(3, n + 1, 4) if is_Motzkin(m, m // 2)]
A095100_list(363) # Peter Luschny, Aug 08 2012
(PARI) isok(m) = {if(m%4<3, return(0)); my(s=0); for(i=1, m-1, if((s+=kronecker(i, m))<0, return(0))); 1; } \\ Jinyuan Wang, Jul 20 2020

Crossrefs

Subset of A095102. Complement of A095101 in A004767.

Cf. A095090.

Sequence in context: A246559 A246521 A160785 * A036994 A243115 A279106

Adjacent sequences: A095097 A095098 A095099 * A095101 A095102 A095103

Keyword

nonn

Author

Antti Karttunen, Jun 01 2004

Status

approved