A121982 -id:A121982 - cp's OEIS frontend

A253142 Numbers n such that n + 15 and n^2 + 15 are prime.

2, 4, 8, 14, 16, 22, 26, 32, 38, 44, 46, 52, 64, 68, 86, 88, 98, 124, 134, 158, 178, 184, 196, 212, 236, 242, 248, 256, 262, 296, 298, 316, 322, 338, 364, 374, 386, 394, 452, 472, 484, 488, 548, 578, 586, 598, 602, 626, 632, 638, 646, 658, 662, 676, 694, 718, 728, 736, 794, 806, 842, 848, 862

Offset: 1

Zak Seidov, Dec 27 2014

nonn

			2 + 15 = 17 and 2^2 + 15 = 19 are both prime, so 2 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Intersection of A086303 and A121982.

select(t -> isprime(t+15) and isprime(t^2+15), [seq(i,i=2..1000,2)]); # Robert Israel, May 07 2019

p = 15; Select[Range[2,1000,2], PrimeQ[p + #^2] && PrimeQ[p + #] &]
Select[Range[2,1000,2],AllTrue[{#,#^2}+15,PrimeQ]&] (* Harvey P. Dale, Jun 08 2023 *)

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

A243450 Primes of the form n^2 + 15.

Original entry on oeis.org

19, 31, 79, 211, 271, 499, 691, 1039, 1171, 1459, 1951, 2131, 2719, 4111, 4639, 5791, 7411, 7759, 9619, 10831, 11251, 15391, 17971, 24979, 29599, 31699, 33871, 38431, 40819, 42451, 44959, 55711, 56659, 58579, 61519, 65551, 68659, 73999, 80671, 87631, 88819

Offset: 1

Vincenzo Librandi, Jun 05 2014

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

Cf. A121982 (associated n).

Cf. similar sequences listed in A243449.

[a: n in [0..1000] | IsPrime(a) where a is n^2+15];

Select[Table[n^2 + 15, {n, 0, 1000}], PrimeQ]

list(lim)=my(v=List(),t); forstep(k=2,sqrtint(lim\1-15),2, if(isprime(t=k^2+15), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Nov 06 2024

a(n) >> n^2 log n. - Charles R Greathouse IV, Nov 06 2024

A252783 Numbers n such that n + 15, n^2 + 15, n^3 + 15, n^4 + 15, n^5 + 15 and n^6 + 15 are all prime.

Original entry on oeis.org

2, 4, 10830278, 11409622, 37189336, 41206834, 44438468, 65401492, 67135342, 85329104, 92243452, 110149004, 138651242, 182279216, 205680028, 216904744, 307575212, 309431906, 469311346, 490359076, 527228606, 529432582, 549804952, 572599934, 575037022, 596410214, 599921326, 616509454, 643063226, 679784492, 681657946, 722166524, 736641808, 766101998, 789147538, 824154506, 857134166, 870601984, 878365744, 914746816

Offset: 1

Zak Seidov, Dec 27 2014

nonn

			15 + {2, 4, 8, 16, 32, 64} = {17, 19, 23, 31, 47, 79} all primes.

Zak Seidov, Table of n, a(n) for n = 1..157

Cf. A253166, A253143, A253142, A086303, A121982.

isok(n) = isprime(n+15) && isprime(n^2 + 15) && isprime(n^3 + 15) && isprime(n^4 + 15) && isprime(n^5 + 15) && isprime(n^6 + 15); \\ Michel Marcus, Dec 28 2014

A253143 Numbers n such that n + 15, n^2 + 15 and n^3 + 15 are prime.

Original entry on oeis.org

2, 4, 16, 22, 32, 44, 86, 88, 98, 298, 316, 452, 602, 638, 658, 736, 862, 868, 896, 1276, 1358, 1586, 1768, 1996, 2342, 2366, 2444, 2452, 2542, 2788, 2902, 3242, 3448, 3704, 3718, 3998, 4376, 4552, 4928, 5422, 5504, 5566, 5608, 5644, 5728, 5768, 5776, 6664, 6934, 6946, 7708, 7858

Offset: 1

Zak Seidov, Dec 27 2014

nonn

			With n=2, n+15 (17), n^2+15 (19) and n^3+15 (23) are all prime.

Subsequence of A253142, A086303 and A121982.

p = 15; Select[Range[2, 20000, 2], PrimeQ[p + #^3] && PrimeQ[p + #^2] && PrimeQ[p + #] &]
Select[Range[2,8000,2],AllTrue[#^Range[3]+15,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 29 2018 *)

isok(n) = isprime(n+15) && isprime(n^2 + 15) && isprime(n^3 + 15); \\ Michel Marcus, Dec 28 2014

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

A253166 Numbers n such that n^k+15, with k=1..7, are all prime.

Original entry on oeis.org

599921326, 1107778868, 2011251698, 3589612642, 4811175086, 6153188512

Offset: 1

Zak Seidov, Dec 28 2014

No term (yet) with n^8 + 15 prime.

Subsequence of A252783.

Cf. A253143, A253142, A086303, A121982.

cp's OEIS Frontend

A253142 Numbers n such that n + 15 and n^2 + 15 are prime.

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

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Magma

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A243450 Primes of the form n^2 + 15.

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A252783 Numbers n such that n + 15, n^2 + 15, n^3 + 15, n^4 + 15, n^5 + 15 and n^6 + 15 are all prime.

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PARI

A253143 Numbers n such that n + 15, n^2 + 15 and n^3 + 15 are prime.

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Mathematica

PARI

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

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Magma

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A253166 Numbers n such that n^k+15, with k=1..7, are all prime.

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