cp's OEIS Frontend

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.

%I A095101 #19 May 19 2024 03:19:48
%S A095101 19,43,51,67,91,99,107,115,123,127,139,147,155,163,179,187,195,203,
%T A095101 207,211,219,223,227,235,247,259,267,275,283,291,307,315,323,331,339,
%U A095101 347,355,367,379,387,403,411,423,427,435,443,451,459,463,467
%N 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.
%C A095101 Integers whose Jacobi-vector does not form a valid Motzkin-path.
%H A095101 Antti Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%F A095101 a(n) = 4*A095275(n) + 3.
%o A095101 (Sage)
%o A095101 def is_Motzkin(n, k):
%o A095101     s = 0
%o A095101     for i in (1..k) :
%o A095101         s += jacobi_symbol(i, n)
%o A095101         if s < 0 : return False
%o A095101     return True
%o A095101 def A095101_list(n):
%o A095101     return [m for m in range(3, n+1, 4) if not is_Motzkin(m, m//2)]
%o A095101 A095101_list(467) # _Peter Luschny_, Aug 08 2012
%o A095101 (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
%Y A095101 Subset of A095103. Complement of A095100 in A004767.
%Y A095101 Cf. A095091.
%K A095101 nonn
%O A095101 1,1
%A A095101 _Antti Karttunen_, Jun 01 2004