A038600 -id:A038600 - cp's OEIS frontend

A038599 Numbers k such that k^3 - 2 is prime.

9, 15, 19, 27, 31, 37, 67, 91, 99, 109, 121, 129, 135, 145, 151, 165, 187, 189, 201, 207, 211, 217, 241, 259, 265, 267, 277, 279, 289, 319, 355, 357, 367, 369, 387, 391, 411, 417, 427, 435, 439, 445, 457, 459, 477, 489, 511, 525, 549, 555, 561, 615, 619, 621

Offset: 1

Jeff Burch

nonn

			15^3 - 2 = 3373 is prime, so 15 is in the sequence.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A038600, A028870, A028873.

a[n_]:=n^x-y;lst={};x=3;y=2;Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 03 2009 *)
Select[Range@ 640, PrimeQ[#^3 - 2] &] (* Michael De Vlieger, May 10 2016 *)

is(n)=isprime(n^3-2) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A038600(n)+2)^(1/3). - Zak Seidov, May 10 2016

Missed term, 207, and more terms added by Zak Seidov, Mar 14 2009

A178251 Primes p such that p^3 - 2 is prime.

Original entry on oeis.org

19, 31, 37, 67, 109, 151, 211, 241, 277, 367, 439, 457, 619, 691, 727, 787, 859, 967, 1087, 1171, 1471, 1489, 1531, 1579, 1951, 2131, 2287, 2791, 2851, 2971, 3061, 3319, 3511, 3547, 3559, 3739, 4129, 4357, 4447, 4507, 4591, 4651, 4789, 4801, 4831, 4951

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 24 2010

			6857 = prime(882) = 19^3 - 2, 19 = prime(8) is 1st term.
29789 = prime(3228) = 31^3 - 2, 31 = prime(11) is 2nd term.

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

Cf. A000040, A000578, A038599, A038600, A144953.

[p: p in PrimesUpTo(5000) | IsPrime(p^3-2)]; // Vincenzo Librandi, Nov 17 2010

Select[Prime[Range[10000]], PrimeQ[#^3 - 2] &] (* Vincenzo Librandi, Mar 20 2014 *)

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(p^3-2), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 08 2016

a = list(p for p in primes(10000) if is_prime(p**3-2)) # D. S. McNeil, May 25 2010

Base tag removed by D. S. McNeil, May 25 2010

A178506 Lesser of a "near cube" twin prime pair (k^3 - 4, k^3 - 2).

Original entry on oeis.org

3371, 8120597, 69426527, 108531329, 176558477, 1207949621, 2379270371, 3477265871, 3560550179, 4227952109, 8012005997, 12665630687, 13060888871, 15832158827, 15945922409, 18337088849, 20279414579, 22354272509, 30283802609, 60559558979, 70496180087, 98035951127

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 29 2010

nonn

p + 2 = k^3 - 2 is form of "near(est) cube" prime smaller than cube number k^3, as k^3 - 1 = (k-1) * (k^2 + k + 1), only prime for k=2.

			p = 3371 = prime(475) = 15^3 - 4, (p, p+2) is twin prime pair tp(90), 3371 is the first term.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A178336.

Cf. A001359, A053703, A132282, A144953, A173255, A178228, A038600.

Select[Range[10^4]^3 - 4, And @@ PrimeQ[# + {0, 2}] &] (* Amiram Eldar, Dec 25 2019 *)

a(13) corrected and more terms from Amiram Eldar, Dec 25 2019

A178507 Numbers n that (n^3 - 4,n^3 - 2) is a twin prime pair.

Original entry on oeis.org

15, 201, 411, 477, 561, 1065, 1335, 1515, 1527, 1617, 2001, 2331, 2355, 2511, 2517, 2637, 2727, 2817, 3117, 3927, 4131, 4611, 4755, 4797, 5121, 5427, 5457, 5787, 6045, 6501, 6675, 7347, 7395, 8637, 9591, 9711, 10071, 10305, 10371, 10377, 10965, 11031

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 29 2010

nonn

See A178506.

Necessarily n odd multiple of 3, LSD of n is e = 1, 5 or 7.

			p = 15^3 - 4 = 3371 = prime(475), p+2 = prime(476), 15 is first term.
p = 201^3 - 4 = 8120597 = prime(547310), p+2 = prime(547311), 201 is 2nd term.
p = 15915^3 - 4 = 4031066185871 = prime(i), i = 144036640497, p+2 = prime(i+1), 15915 is another term.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001359, A038600, A178506.

Select[Range[12000],AllTrue[#^3-{4,2},PrimeQ]&] (* Harvey P. Dale, Jul 28 2024 *)

is(n) = isprime(n^3-2) && isprime(n^3-4) \\ Michel Marcus, Jul 22 2013

Term 6045 added by Michel Marcus, Jul 22 2013

A330438 Numbers k such that k^2-2 and k^3-2 are prime.

Original entry on oeis.org

9, 15, 19, 27, 37, 121, 135, 145, 211, 217, 259, 265, 267, 279, 355, 357, 387, 391, 435, 489, 525, 561, 615, 621, 727, 951, 987, 1029, 1119, 1141, 1177, 1251, 1287, 1357, 1435, 1491, 1561, 1617, 1717, 1785, 1819, 1839, 1875, 1909, 1989, 2001, 2077, 2107, 2211

Offset: 1

K. D. Bajpai, Dec 14 2019

nonn

Intersection of A028870 and A038599.

			a(1) = 9: 9^2 - 2 = 79; 9^3 - 2 = 727; both results are prime.
a(2) = 15: 15^2 - 2 = 223; 15^3 - 2 = 3373; both results are prime.

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

Cf. A028870, A028873, A038599, A038600, A108701.

[n : n in [1 .. 100] | IsPrime (n^2 - 2) and IsPrime (n^3 - 2)];

filter:= k -> isprime(k^2-2) and isprime(k^3-2):
select(filter, [$2..10000]); # Robert Israel, Dec 24 2019

Select[Range[10000], PrimeQ[#^3 - 2] && PrimeQ[#^2 - 2] &]

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A038599 Numbers k such that k^3 - 2 is prime.

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A178251 Primes p such that p^3 - 2 is prime.

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A178506 Lesser of a "near cube" twin prime pair (k^3 - 4, k^3 - 2).

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A178507 Numbers n that (n^3 - 4,n^3 - 2) is a twin prime pair.

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A330438 Numbers k such that k^2-2 and k^3-2 are prime.

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