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A095100 Integers n of the form 4k+3 for which all sums Sum_{i=1..u} J(i/n) (with u ranging from 1 to (n-1)) are nonnegative, where J(i/n) is Jacobi symbol of i and n. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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

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-Fran├žois Alcover, Oct 08 2013, translated from Sage *)

PROG

(Sage)

def A095100_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

    return filter(lambda m: is_Motzkin(m, m//2), range(n+1)[3::4])

A095100_list(363) # Peter Luschny, Aug 08 2012

CROSSREFS

a(n) = 4*A095274(n)+3.Subset: 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 and Jun 01 2004

STATUS

approved

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Last modified December 11 15:43 EST 2017. Contains 295905 sequences.