A332021 -id:A332021 - cp's OEIS frontend

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

1, 4, 5, 9, 12, 14, 16, 17, 19, 20, 22, 23, 25, 29, 30, 31, 34, 35, 36, 37, 38, 40, 42, 43, 46, 47, 49, 51, 53, 57, 59, 61, 63, 64, 66, 67, 70, 72, 73, 76, 77, 78, 80, 81, 82, 86, 87, 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

Offset: 1

Zhi-Wei Sun, Feb 04 2020

nonn

Clearly, the sequence contains all positive squares.

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.

			a(1) = 1 since 1 is a quadratic residue modulo prime(1) = 2.
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.

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Cf. A000040, A000290, A242750, A332021.

tab = {}; Do[If[JacobiSymbol[n, Prime[n]] == 1, tab = Append[tab, n]], {n, 140}]; tab

isok(m) = kronecker(m, prime(m)) == 1; \\ Michel Marcus, Feb 06 2020

cp's OEIS Frontend

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

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