A121250 -id:A121250 - cp's OEIS frontend

A121982 Numbers k such that k^2 + 15 is prime.

2, 4, 8, 14, 16, 22, 26, 32, 34, 38, 44, 46, 52, 64, 68, 76, 86, 88, 98, 104, 106, 124, 134, 158, 172, 178, 184, 196, 202, 206, 212, 236, 238, 242, 248, 256, 262, 272, 284, 296, 298, 304, 316, 322, 326, 328, 338, 356, 362, 364, 374, 386, 388, 394, 398, 452, 472

Offset: 1

Parthasarathy Nambi, Sep 09 2006

			If k=104 then k^2 + 15 = 10831 (prime).

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A005574, A067201, A049422, A007591, A078402, A114269, A114271, A114272, A114273, A114274, A114275, A113536, A121250.

[n: n in [0..6000] | IsPrime(n^2 + 15)]; // Vincenzo Librandi, Nov 13 2010

Select[Range[200], PrimeQ[#1^2 + 15] &] (* G. C. Greubel, Sep 13 2017 *)

is(n)=isprime(n^2+15) \\ Charles R Greathouse IV, Feb 17 2017

A122062 Numbers k such that k^2 + 16 is prime.

Original entry on oeis.org

1, 5, 9, 11, 15, 21, 25, 29, 31, 41, 49, 51, 55, 65, 75, 79, 81, 89, 91, 95, 99, 109, 115, 119, 121, 125, 129, 151, 165, 179, 191, 211, 219, 221, 229, 231, 245, 249, 265, 275, 281, 289, 291, 295, 299, 301, 311, 315, 335, 351, 355, 361, 365, 369, 381, 389, 391

Offset: 1

Parthasarathy Nambi, Sep 14 2006

nonn

			If k=99 then k^2 + 16 = 9817 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..5000

Cf. A005574, A067201, A049422, A007591, A078402, A114269, A114271, A114272, A114273, A114274, A114275, A113536, A121250, A121982.

[n: n in [0..6000] | IsPrime(n^2 + 16)]; // Vincenzo Librandi, Nov 13 2010

Select[Range[1,501,2],PrimeQ[16+#^2]&] (* Harvey P. Dale, Dec 04 2018 *)

is(n)=isprime(n^2+16) \\ Charles R Greathouse IV, Jun 06 2017

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 *)

A264790 Numbers k such that k^2 + 17 is prime.

Original entry on oeis.org

0, 6, 24, 60, 66, 78, 90, 108, 144, 162, 174, 186, 234, 252, 294, 300, 318, 330, 336, 342, 372, 396, 420, 438, 456, 462, 468, 498, 528, 594, 636, 648, 654, 672, 720, 750, 798, 804, 834, 858, 888, 924, 930, 966, 984, 990, 1014, 1026, 1032, 1086, 1158, 1194, 1200

Offset: 1

Ilya Gutkovskiy, Nov 25 2015

nonn

Primes of the form k^2 + 17 have a representation as a sum of 2 squares because they belong to A002144.

All terms are multiple of 6.

			a(3) = 24 because 24^2 + 17 = 593, which is prime.

Daniel Starodubtsev, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Near-Square Prime

Cf. A228244 (associated primes).

Other sequences of the type "Numbers n such that n^2 + k is prime": A005574 (k=1), A067201 (k=2), A049422 (k=3), A007591 (k=4), A078402 (k=5), A114269 (k=6), A114270 (k=7), A114271 (k=8), A114272 (k=9), A114273 (k=10), A114274 (k=11), A114275 (k=12), A113536 (k=13), A121250 (k=14), A121982 (k=15), A122062 (k=16).

[n: n in [0..1200 ] | IsPrime(n^2+17)]; // Vincenzo Librandi, Nov 25 2015

Select[Range[0, 1200], PrimeQ[#^2 + 17] &] (* Michael De Vlieger, Nov 25 2015 *)

for(n=0, 1e3, if(isprime(n^2+17), print1(n, ", "))) \\ Altug Alkan, Nov 25 2015

A000005(A241847(a(n))) = 2.

A241847(a(n)) = A228244(n).

Edited by Bruno Berselli, Nov 26 2015

A121817 Numbers m such that 23 + 36m(m+1) is prime.

Original entry on oeis.org

0, 2, 4, 5, 7, 12, 14, 15, 27, 30, 32, 34, 40, 47, 49, 50, 57, 60, 62, 67, 72, 75, 82, 85, 89, 95, 97, 102, 104, 105, 109, 110, 119, 135, 140, 162, 175, 177, 180, 182, 187, 189, 194, 200, 214, 219, 222, 225, 235, 239, 242, 244, 247, 254, 257, 259, 265, 277, 279, 280

Offset: 1

Zak Seidov, Sep 09 2006

nonn

All terms of A121250 (numbers n such that n^2+14 is prime) are of the form n = 3+6*m, m = 0, 1, .... Hence n^2 + 14 = 23 + 36*m(m+1): these values of m are in this sequence.

Cf. A121250.

Select[Range[0,300], PrimeQ[23 + 36*#(1+#) ]&]

select( is_A121817(n)=isprime(23+36*(n+1)*n), [0..299]) \\ M. F. Hasler, May 25 2019

Edited by M. F. Hasler, May 25 2019

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A121982 Numbers k such that k^2 + 15 is prime.

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A122062 Numbers k such that k^2 + 16 is prime.

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A243449 Primes of the form n^2 + 14.

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A264790 Numbers k such that k^2 + 17 is prime.

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A121817 Numbers m such that 23 + 36*m*(m+1) is prime.

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A121817 Numbers m such that 23 + 36m(m+1) is prime.