A237437 Least prime p > prime(n+1) such that p is not a square mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1).

5, 17, 17, 17, 83, 167, 167, 227, 2273, 5297, 5297, 69467, 69467, 116387, 348563, 348563, 2004917, 5472953, 8062073, 8062073

Offset

1,1

Comments

Least prime p > prime(n+1) such that p is a quadratic nonresidue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1).

Least odd prime p such that the Legendre symbol (p|q) = -1 for q = 3, 5, 7, 11, ..., prime(n+1).

Links

Table of n, a(n) for n=1..20.

Wipawee Tangjai, Kodchaphon Wanichang, Montathip Srikao, and Punyanuch Kheawkrai, A Congruent Property of Gibonacci Number Modulo Prime, Int'l. J. Analysis Appl. (2023), Vol. 21, No. 24.

Wikipedia, Legendre symbol

Wikipedia, Quadratic residue

Formula

a(n) = a(n+1) if and only if Legendre (a(n)|prime(n+2)) = -1.

Example

Let f(p) = list of Legendre (p|q) for q = 3, 5, 7, 11, 13, 17, 19, 23, ...
Then f(p) is
p=3: 0, -1, -1, 1, 1, -1, -1, 1, ...
p=5: -1, 0, -1, 1, -1, -1, 1, -1, ...
p=7: 1, -1, 0, -1, -1, -1, 1, -1, ...
p=11: -1, 1, 1, 0, -1, -1, 1, -1, ...
p=13: 1, -1, -1, -1, 0, 1, -1, 1, ...
p=17: -1, -1, -1, -1, 1, 0, 1, -1, ...
p=19: 1, 1, -1, -1, -1, 1, 0, -1, ...
f(5) is the first list that begins with -1, so a(1) = 5.
f(17) is the first list that begins with -1, -1, so a(2) = 17.

Mathematica

Table[p = Prime[n + 2]; While[Length[Select[Prime[Range[2, n + 1]], JacobiSymbol[p, #] == -1 &]] < n, p = NextPrime[p]]; p, {n, 1, 20}]

Crossrefs

Cf. A237436.

Sequence in context: A303678 A303804 A304851 * A128895 A141558 A304217

Adjacent sequences: A237434 A237435 A237436 * A237438 A237439 A237440

Keyword

nonn

Author

Jonathan Sondow, Feb 15 2014

Status

approved