A079138 -id:A079138 - cp's OEIS frontend

A228244 Primes of the form k^2 + 17.

17, 53, 593, 3617, 4373, 6101, 8117, 11681, 20753, 26261, 30293, 34613, 54773, 63521, 86453, 90017, 101141, 108917, 112913, 116981, 138401, 156833, 176417, 191861, 207953, 213461, 219041, 248021, 278801, 352853, 404513, 419921, 427733, 451601, 518417, 562517

Offset: 1

Michel Marcus, Aug 18 2013

			17 = 0^2 + 17 is prime.
53 = 6^2 + 17 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A049423, A056899, A056905, A079138, A138362, A138375, A241847, A264790.

[m: n in [0..900] | IsPrime(m) where m is n^2+17]; // Bruno Berselli, Aug 18 2013

Select[Table[n^2 + 17, {n, 0, 900}], PrimeQ] (* Bruno Berselli, Aug 18 2013 *)

PARI
```
isp(n) = isprime(n) && issquare(n-17);
```

a(n) = A241847(A264790(n)). - Elmo R. Oliveira, Apr 21 2025

A243449 Primes of the form n^2 + 14.

Original entry on oeis.org

23, 239, 743, 1103, 2039, 5639, 7583, 8663, 27239, 33503, 38039, 42863, 59063, 81239, 88223, 91823, 119039, 131783, 140639, 164039, 189239, 205223, 245039, 263183, 288383, 328343, 342239, 378239, 393143, 400703, 431663, 439583, 514103, 660983, 710663, 950639

Offset: 1

Vincenzo Librandi, Jun 05 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A121250 (associated n).

Cf. primes of the form n^2+k: A144255 (k=1), A056899 (k=2), A049423 (k=3), A005473 (k=4), A056905 (k=5), A056909 (k=6), A079138 (k=7), A138338 (k=8), A138353 (k=9), A138355 (k=10), A138362 (k=11), A138368 (k=12), A138375 (k=13), this sequence (k=14), A243450 (k=15), A243451 (k=16), A228244 (k=17), A174812 (k=42).

[a: n in [0..1000] | IsPrime(a) where a is n^2+14];

Select[Table[n^2 + 14, {n, 0, 2000}], PrimeQ]
Select[Range[1,1001,2]^2+14,PrimeQ] (* Harvey P. Dale, May 30 2023 *)

cp's OEIS Frontend

A228244 Primes of the form k^2 + 17.

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