A095101 - OEIS

%I #19 May 19 2024 03:19:48

%S 19,43,51,67,91,99,107,115,123,127,139,147,155,163,179,187,195,203,

%T 207,211,219,223,227,235,247,259,267,275,283,291,307,315,323,331,339,

%U 347,355,367,379,387,403,411,423,427,435,443,451,459,463,467

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

%H Antti Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%F a(n) = 4*A095275(n) + 3.

%o (Sage)

%o def is_Motzkin(n, k):

%o     s = 0

%o     for i in (1..k) :

%o         s += jacobi_symbol(i, n)

%o         if s < 0 : return False

%o     return True

%o def A095101_list(n):

%o     return [m for m in range(3, n+1, 4) if not is_Motzkin(m, m//2)]

%o A095101_list(467) # _Peter Luschny_, Aug 08 2012

%o (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 Subset of A095103. Complement of A095100 in A004767.

%Y Cf. A095091.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 01 2004