A243893 a(n) = prime(k-1) with k = n^2 + prime(n)^2.

7, 37, 137, 311, 829, 1249, 2269, 2939, 4483, 7411, 8681, 12653, 15877, 17827, 21673, 28087, 35393, 38317, 46957, 53327, 56897, 67493, 75269, 87523, 105143, 115057, 120427, 130811, 136547, 147863, 189067, 202481, 222991, 230393, 267401, 275677

Offset: 1

Author

Freimut Marschner, Jun 14 2014

Keywords

• nonn

Comments

prime(k-1) is also the largest prime number < (n^2 + prime(n)^2). Remark : Largest prime number < n^2 is A053001. Largest prime number < n^3 is A077037.

Examples

			n=1, 1^2=1, prime(1)^2 = 4, 1 + 4 = 5, 5 - 1= 4, prime(4) = 7 ;
n=2, 2^2=4, prime(2)^2 = 9, 4 + 9= 13, 13 - 1= 12, prime(12) = 37.
		

Links

• Freimut Marschner, Table of n, a(n) for n = 1..63

Crossrefs

Cf. A000290 (squares n^2), A000040 (prime(n)), A001248 (prime(n)^2), A106587 (n^2 + prime(n)^2).

Programs

Mathematica

a[n_]:=Prime[(n^2 + Prime[n]^2) - 1]; Array[a,36] (* Stefano Spezia, Mar 12 2025 *)

Formula

a(n) = prime((n^2 + prime(n)^2) - 1) = prime(A106587(n) - 1).