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.
19, 43, 51, 67, 91, 99, 107, 115, 123, 127, 139, 147, 155, 163, 179, 187, 195, 203, 207, 211, 219, 223, 227, 235, 247, 259, 267, 275, 283, 291, 307, 315, 323, 331, 339, 347, 355, 367, 379, 387, 403, 411, 423, 427, 435, 443, 451, 459, 463, 467
Offset: 1
Keywords
Links
- Antti Karttunen and J. Moyer, C-program for computing the initial terms of this sequence
Programs
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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 -
Sage
def is_Motzkin(n, k): s = 0 for i in (1..k) : s += jacobi_symbol(i, n) if s < 0 : return False return True def A095101_list(n): return [m for m in range(3, n+1, 4) if not is_Motzkin(m, m//2)] A095101_list(467) # Peter Luschny, Aug 08 2012
Formula
a(n) = 4*A095275(n) + 3.
Comments