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A332020 Positive integers m which are quadratic residues modulo prime(m).

%I A332020 #19 Feb 07 2020 11:44:01
%S A332020 1,4,5,9,12,14,16,17,19,20,22,23,25,29,30,31,34,35,36,37,38,40,42,43,
%T A332020 46,47,49,51,53,57,59,61,63,64,66,67,70,72,73,76,77,78,80,81,82,86,87,
%U A332020 89,91,92,94,96,97,98,99,100,102,103,104,105,106,111,112,113,115,121,125,127,128,132,134,136,137,138,140
%N A332020 Positive integers m which are quadratic residues modulo prime(m).
%C A332020 Clearly, the sequence contains all positive squares.
%C A332020 Conjecture: Let A(x) be the number of terms not exceeding x. Then A(x)/x has the limit 1/2 as x tends to the infinity.
%H A332020 Zhi-Wei Sun, <a href="/A332020/b332020.txt">Table of n, a(n) for n = 1..10000</a>
%e A332020 a(1) = 1 since 1 is a quadratic residue modulo prime(1) = 2.
%e A332020 a(2) = 4 since 4 is a quadratic residue modulo prime(4) = 7, but 2 is a quadratic nonresidue modulo prime(2) = 3, and 3 is a quadratic nonresidue modulo prime(3) = 5.
%t A332020 tab = {}; Do[If[JacobiSymbol[n, Prime[n]] == 1, tab = Append[tab, n]], {n, 140}]; tab
%o A332020 (PARI) isok(m) = kronecker(m, prime(m)) == 1; \\ _Michel Marcus_, Feb 06 2020
%Y A332020 Cf. A000040, A000290, A242750, A332021.
%K A332020 nonn
%O A332020 1,2
%A A332020 _Zhi-Wei Sun_, Feb 04 2020