A243894 a(n) = prime(k+1) with k = n^2 + prime(n)^2.

13, 43, 149, 317, 853, 1277, 2281, 2957, 4507, 7433, 8693, 12671, 15887, 17839, 21701, 28099, 35407, 38327, 46997, 53359, 56911, 67511, 75289, 87541, 105173, 115067, 120473, 130829, 136573, 147919, 189139, 202519, 223009, 230449, 267413, 275711

Offset: 1

Author

Freimut Marschner, Jun 14 2014

Keywords

• nonn

Comments

The prime numbers prime(k-1) = A243893, prime(k) = A243892 and a(n) = prime(k+1) with k = n^2 + prime(n)^2 are forming a triple of successive prime numbers.

Examples

			n=1, n^2 = 1, prime(1) = 2, 2^2 = 4, 1 + 4 = 5, 5 + 1 = 6, prime(6) = 13 ;
n=2, n^2 = 4, prime(2) = 3, 3^2 = 9, 4 + 9 = 13, 13 + 1 = 14, prime(14) = 43.
		

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

Table[Prime[n^2+Prime[n]^2+1],{n,40}] (* Harvey P. Dale, Dec 31 2015 *)

PARI

vector(40, n, prime(n^2 + prime(n)^2 + 1)) \\ Colin Barker, Jun 14 2014

Formula

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