A187873 Second smallest prime after n^2.

3, 3, 7, 13, 19, 31, 41, 59, 71, 89, 103, 131, 151, 179, 199, 229, 263, 307, 337, 373, 409, 449, 491, 547, 587, 641, 683, 739, 797, 857, 911, 971, 1033, 1093, 1171, 1231, 1301, 1381, 1451, 1531, 1607, 1697, 1783, 1867, 1951, 2029

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Mar 14 2011

Keywords

• nonn

Comments

From Robert Israel, Dec 18 2018: (Start)

Oppermann's conjecture implies a(n) < (n+1)^2 for n > 0.

For n > 1, a(n) >= n^2 + 3, with equality for n in A080149. (End)

Examples

			2^2=4, second smallest prime=7;
3^2=9, second smallest prime=13; ..
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Wikipedia, Oppermann's conjecture

Crossrefs

Cf. A007491, A014210, A080149.

Programs

Maple

seq(nextprime(nextprime(n^2)),n=0..50); # Robert Israel, Dec 18 2018

Mathematica

NextPrime[Range[0,100]^2, 2]