A243896 a(n) = prime(n^2+1).

2, 3, 11, 29, 59, 101, 157, 229, 313, 421, 547, 673, 829, 1013, 1201, 1429, 1621, 1889, 2153, 2441, 2749, 3089, 3463, 3821, 4217, 4639, 5059, 5521, 6011, 6491, 7001, 7577, 8167, 8741, 9343, 9941, 10631, 11329, 12071, 12757, 13513, 14341, 15107, 15881

Offset: 0

Author

Freimut Marschner, Jun 17 2014

Keywords

• nonn

Comments

For n>1, the numbers prime(n^2-1), prime(n^2) and prime(n^2+1), that is, A243895(n), A001248(n) and a(n), constitute a triple of successive prime numbers.

Examples

			n = 4, n^2 = 16, n^2 + 1 = 17, prime(17) = 59.
		

Links

• Freimut Marschner, Table of n, a(n) for n = 0..97

Crossrefs

Cf. A000290 (squares n^2), A000040 (prime(n)), A001248 (prime(n)^2). A011757 (prime(n^2)), A055875 (prime(n^3)), A096327 (prime((prime(n)^2))), A096328 (prime(prime(n)^3)), A038580 (prime(prime(prime(n)))).

Programs

Mathematica

Table[Prime[n^2+1],{n,0,50}] (* Harvey P. Dale, Dec 25 2022 *)

Formula

a(n) = prime(n^2 + 1) = prime(A000290(n) + 1) = prime(A002522(n)).