A166049 Integers of the form 4n+1 for which Sum_{i=1..u} J(i,4n+1) is never negative for any u in range [1,(2n)], where J(i,k) is the Jacobi symbol.
1, 5, 9, 13, 21, 25, 37, 49, 81, 85, 93, 121, 165, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241
Offset: 1
Keywords
Programs
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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 A166049_list(n): return [m for m in range(1, n + 1, 4) if is_Motzkin(m, m // 2)] A166049_list(6241) # Peter Luschny, Aug 08 2012