login
Nonnegative numbers k such that 0 = #{ 0 <= i <= k : K(k, i) = -1 } where K(k, i) is the Kronecker symbol.
2

%I #21 May 17 2024 04:56:54

%S 0,1,2,4,6,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,

%T 361,400,441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,

%U 1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401

%N Nonnegative numbers k such that 0 = #{ 0 <= i <= k : K(k, i) = -1 } where K(k, i) is the Kronecker symbol.

%C Contains all squares.

%C These are the indices of the rows of A372728 with nonnegative terms. - _Peter Luschny_, May 16 2024

%C Apparently, 2 and 6 are the only nonsquares in the sequence. - _Hugo Pfoertner_, May 16 2024

%t Reap[For[n = 0, n < 2500, n++, If[NoneTrue[Range[n], KroneckerSymbol[n, #] == -1&], Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Nov 18 2016 *)

%o (SageMath)

%o print([n for n in range(999) if 0 == sum(kronecker(n, k) == -1

%o for k in range(n + 1))]) # _Peter Luschny_, May 16 2024

%Y Cf. A000010, A051953, A372728.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Aug 06 2004

%E 0 prepended by _Peter Luschny_, May 16 2024