A374155 a(n) is the least prime that is a quadratic residue modulo prime(n). First column of A373751.

2, 3, 5, 2, 3, 3, 2, 5, 2, 5, 2, 3, 2, 11, 2, 7, 3, 3, 17, 2, 2, 2, 3, 2, 2, 5, 2, 3, 3, 2, 2, 3, 2, 5, 5, 2, 3, 41, 2, 13, 3, 3, 2, 2, 7, 2, 5, 2, 3, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 17, 7, 2, 2, 7, 5, 2, 3, 3, 2, 2, 2, 3, 5, 2, 5, 3, 2, 2, 3, 3, 2, 2, 2

Offset: 1

Author

Peter Luschny, Jun 29 2024

Keywords

• nonn

Examples

			a(38) = 41 because row 38 of A373751 starts 41, 43, 47, ..., which are the primes that are quadratic residues modulo 163.
		

Crossrefs

Variant: A306530 (differs in the first 3 values).

Cf. A373751.

Programs

Maple

a := proc(n) local a, p; a := 1; p := ithprime(n); while true do a := a + 1;
if NumberTheory:-QuadraticResidue(a, p) = 1 and isprime(a) then return a fi od end: seq(a(n), n = 1..85);

PARI

a(n) = my(p=prime(n), q=2); while (!issquare(Mod(q, p)), q=nextprime(q+1)); q; \\ Michel Marcus, Jun 29 2024