A243895 a(n) = prime(n^2-1).

5, 19, 47, 89, 149, 223, 307, 409, 523, 659, 823, 997, 1187, 1423, 1613, 1877, 2141, 2423, 2731, 3079, 3457, 3797, 4201, 4621, 5039, 5507, 5987, 6473, 6991, 7561, 8147, 8731, 9337, 9929, 10613, 11317, 12043, 12739, 13487, 14323, 15091, 15859, 16741

Offset: 2

Author

Freimut Marschner, Jun 17 2014

Keywords

• nonn

Comments

The prime numbers prime(k-1), prime(k) = A001248 and prime(k+1) = A243896 with k = n^2 are building a triple of successive prime numbers. Remark: prime(n^2-1) is not defined for n=1.

Examples

			n = 3, n^2 = 9, n^2-1 = 8, prime(8) = 19.
		

Links

• Freimut Marschner, Table of n, a(n) for n = 2..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,2,50}] (* Harvey P. Dale, Jul 16 2025 *)

Formula

a(n) = prime(n^2-1) = prime(A000290(n) - 1) = prime(A005563(n-1)).