A096327 -id:A096327 - cp's OEIS frontend

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

Freimut Marschner, Jun 17 2014

nonn

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.

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

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

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)))).

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

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

A243892 a(n) = prime(k) with k = n^2 + prime(n)^2.

Original entry on oeis.org

11, 41, 139, 313, 839, 1259, 2273, 2953, 4493, 7417, 8689, 12659, 15881, 17837, 21683, 28097, 35401, 38321, 46993, 53353, 56909, 67499, 75277, 87539, 105167, 115061, 120431, 130817, 136559, 147881, 189127, 202493

Offset: 1

Freimut Marschner, Jun 14 2014

nonn

			n = 1, prime(1^2+prime(1)^2) = prime(1 + 2^2) = prime(5) = 11.
n = 2, prime(2^2+prime(2)^2) = prime(4 + 3^2) = prime(13) = 41.

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

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

Also A011757 is prime(n^2), A096327 is prime(prime(n)^2).

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

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

Original entry on oeis.org

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

Freimut Marschner, Jun 17 2014

nonn

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.

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

Freimut Marschner, Table of n, a(n) for n = 2..97

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)))).

Table[Prime[n^2-1],{n,2,50}] (* Harvey P. Dale, Jul 16 2025 *)

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

cp's OEIS Frontend

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

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A243892 a(n) = prime(k) with k = n^2 + prime(n)^2.

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

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