A097698 -id:A097698 - cp's OEIS frontend

A176681 Numbers k such that k^2 +-5 are primes.

6, 12, 36, 72, 78, 168, 198, 204, 342, 432, 456, 492, 534, 588, 594, 666, 726, 756, 786, 804, 996, 1014, 1212, 1218, 1248, 1254, 1266, 1314, 1344, 1476, 1512, 1554, 1806, 1812, 1902, 2088, 2298, 2322, 2364, 2616, 2634, 3066, 3072, 3162, 3432, 3444, 3852

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			12 is in the sequence, because 12^2 + 5 = 149 and 12^2 - 5 = 139 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A097698, A108701

Select[Range[8! ],PrimeQ[ #^2-5]&&PrimeQ[ #^2+5]&]

A176682 Numbers k such that k^2 +-7 are primes.

Original entry on oeis.org

6, 12, 18, 36, 48, 60, 66, 132, 138, 162, 186, 192, 216, 228, 270, 330, 360, 366, 408, 468, 474, 582, 606, 642, 678, 708, 744, 792, 1086, 1182, 1236, 1308, 1326, 1458, 1524, 1686, 1782, 1902, 1998, 2040, 2124, 2178, 2208, 2244, 2358, 2370, 2634, 2658, 2760

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			12 is in the sequence, because 12^2 - 7 = 137 and 12^2 + 7 = 151 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A097698, A108701, A176681

Select[Range[8! ],PrimeQ[ #^2-7]&&PrimeQ[ #^2+7]&]

A176683 Numbers k such that k^2 +-11 are primes.

Original entry on oeis.org

90, 120, 210, 270, 300, 510, 690, 720, 780, 960, 1200, 2190, 4260, 4350, 4470, 4920, 4980, 5040, 5100, 5250, 5550, 5670, 5730, 5790, 6810, 8100, 8280, 8490, 8610, 9150, 9540, 9990, 10140, 10200, 10650, 11130, 11430, 12060, 12510, 12930, 13770, 13800

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			90 is in the sequence, because 90^2 - 11 = 8089 and 90^2 + 11 = 8111 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A097698, A108701, A176681, A176682

Select[Range[8! ],PrimeQ[ #^2-11]&&PrimeQ[ #^2+11]&]
Select[Range[14000],AllTrue[#^2+{11,-11},PrimeQ]&] (* Harvey P. Dale, Aug 03 2024 *)

A097697 Numbers k such that 4*k^2 + 3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 11, 14, 19, 25, 26, 31, 32, 35, 37, 38, 46, 47, 53, 56, 61, 65, 67, 70, 73, 77, 79, 80, 86, 89, 109, 115, 121, 122, 124, 128, 137, 143, 149, 152, 158, 161, 163, 170, 175, 178, 182, 184, 199, 203, 208, 212, 215, 217, 220, 229, 235, 236, 242, 254, 256

Offset: 1

Carl R. White, Aug 20 2004

Cf. A083022, A097698.

[n: n in [1..1000] |IsPrime(4*n^2+3)]; // Vincenzo Librandi, Nov 16 2010

is(n)=isprime(4*n^2+3) \\ Charles R Greathouse IV, Jun 05 2017

A176684 Numbers k such that k^3 +-5 are primes.

Original entry on oeis.org

2, 12, 48, 66, 78, 126, 192, 324, 576, 738, 858, 1806, 2466, 2496, 2688, 3186, 3276, 3978, 4092, 4248, 4404, 4884, 5034, 5274, 5352, 5898, 6018, 6198, 6396, 6408, 6516, 6708, 6852, 7368, 7914, 8304, 8628, 8658, 8904, 9048, 9168, 9528, 10812, 10932

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			12 is in the sequence, because 12^3 - 5 = 1723 and 12^3 + 5 = 1733 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683

Select[Range[8! ],PrimeQ[ #^3-5]&&PrimeQ[ #^3+5]&]

A176685 Numbers k such that k^3 +-7 are primes.

Original entry on oeis.org

36, 114, 174, 264, 426, 444, 810, 894, 900, 2724, 3876, 4140, 4386, 4446, 4686, 4884, 5910, 5940, 6240, 6294, 6534, 6624, 7044, 7206, 7314, 7326, 7470, 8076, 8676, 9120, 9216, 9270, 9546, 9900, 10926, 11040, 11934, 12114, 12510, 14004, 14034, 14100

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			36 is in the sequence, because 36^3 - 7 = 46649 and 36^3 + 7 = 46663 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683, A176684

Select[Range[8! ],PrimeQ[ #^3-7]&&PrimeQ[ #^3+7]&]
Select[Range[15000],AllTrue[#^3+{7,-7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 28 2020 *)

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A176681 Numbers k such that k^2 +-5 are primes.

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A176682 Numbers k such that k^2 +-7 are primes.

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A176683 Numbers k such that k^2 +-11 are primes.

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Mathematica

A097697 Numbers k such that 4*k^2 + 3 is prime.

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A176684 Numbers k such that k^3 +-5 are primes.

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Programs

Mathematica

A176685 Numbers k such that k^3 +-7 are primes.

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Mathematica