A201715 -id:A201715 - cp's OEIS frontend

A201716 Primes of the form 3*m^2 - 4.

23, 71, 239, 359, 503, 863, 1319, 1583, 1871, 2879, 3671, 5039, 8423, 9743, 11159, 11903, 12671, 13463, 16871, 17783, 18719, 20663, 25943, 29399, 33071, 38303, 39671, 48383, 49919, 51479, 61343, 68399, 70223, 73943, 81671, 83663, 87719

Offset: 1

Vincenzo Librandi, Dec 04 2011

Primes p such that 3*(p+4) or (p+4)/3 is a square. - Vincenzo Librandi, Dec 05 2015, Feb 16 2016

			23 is in the sequence because 3 * 3^2 - 4 = 27 - 4 = 23.
71 = 3 * 5^2 - 4.
143 is not in the sequence, because 3 * 7^2 - 4 = 143 but 11 * 13 = 143.

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A089682, A201715, A201717, A201718, A201781.

[a: n in [1..300] | IsPrime(a) where a is 3*n^2-4];

select(isprime, [seq(3*(2*k+1)^2-4, k = 1..1000)]); # Robert Israel, Nov 09 2014

Select[Table[3n^2 - 4, {n, 1000}], PrimeQ]

lista(nn) = for (k=0, nn, if (isprime(p=3*k^2-4), print1(p, ", "))); \\ Michel Marcus, Nov 19 2014, Feb 16 2016

A201717 Primes of the form 3*m^2 - 5.

Original entry on oeis.org

7, 43, 103, 967, 1447, 1723, 2347, 3067, 3463, 4327, 6343, 6907, 9403, 11527, 13063, 21163, 23227, 28807, 32443, 33703, 44647, 47623, 52267, 65707, 71143, 74887, 80683, 88747, 90823, 99367, 110587, 137383, 142567, 150523, 175687

Offset: 1

Vincenzo Librandi, Dec 05 2011

Primes p such that 3*(p+5) or (p+5)/3 is a square. - Vincenzo Librandi, Feb 16 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A000040, A042993 (supersequence).

Cf. similar sequences: A089682, A201715, A201716, A201718, A201781.

[a: n in [2..300] | IsPrime(a) where a is 3*n^2-5];

Mathematica
```
Select[Table[3n^2-5,{n,2,1000}],PrimeQ]
```

A201718 Primes of the form 3*m^2 - 7.

Original entry on oeis.org

5, 41, 101, 293, 761, 1193, 1721, 2693, 3461, 3881, 4793, 5801, 8741, 12281, 16421, 17321, 26501, 32441, 36293, 40361, 53861, 62201, 67493, 80681, 86693, 90821, 92921, 101561, 108293, 112901, 119993, 127301, 145193, 167081, 178601, 193541

Offset: 1

Vincenzo Librandi, Dec 05 2011

Primes p such that (p+7)/3 or 3*(p+7) is a square. - Vincenzo Librandi, Feb 16 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A089682, A201715, A201716, A201717, A201781.

[a: n in [2..300] | IsPrime(a) where a is 3*n^2-7];

Select[Table[3 n^2 - 7, {n, 2, 1000}], PrimeQ]

A201781 Primes of the form 3*m^2 - 8.

Original entry on oeis.org

19, 67, 139, 499, 859, 1579, 1867, 2179, 3259, 4099, 6067, 6619, 8419, 9067, 9739, 22699, 25939, 27067, 28219, 38299, 39667, 46867, 54667, 56299, 61339, 63067, 73939, 79699, 81667, 89779, 91867, 93979, 100459, 102667, 114067, 123619

Offset: 1

Vincenzo Librandi, Dec 05 2011

m is a member of A063241. - Bruno Berselli, Feb 16 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A089682, A201715, A201716, A201717, A201718.

[a: n in [2..300] | IsPrime(a) where a is 3*n^2-8];

Select[Table[3n^2 - 8, {n, 2, 1000}], PrimeQ]

A276261 Centered 21-gonal primes.

Original entry on oeis.org

127, 211, 757, 2521, 2857, 6301, 8527, 16381, 19867, 23689, 24697, 27847, 32341, 37171, 38431, 42337, 66361, 68041, 82237, 89839, 97777, 103951, 114661, 140071, 152461, 162751, 170689, 192781, 204331, 216217, 231547, 240997, 284131, 308827, 353557, 357421, 385057, 389089

Offset: 1

Ilya Gutkovskiy, Aug 26 2016

nonn

Primes of the form (21*k^2 + 21*k + 2)/2.

Numbers k such that (21*k^2 + 21*k + 2)/2 is prime: 3, 4, 8, 15, 16, 24, 28, 39, 43, 47, 48, 51, 55, 059, 60, 63, 79, 80, 88, 92, 96, 99, ...

OEIS Wiki, Centered polygonal numbers
Eric Weisstein's World of Mathematics, Centered Polygonal Number
Index entries for sequences related to centered polygonal numbers

Cf. A000040, A069178.

Cf. similar sequences of the centered k-gonal primes: A125602 (k = 3), A027862 (k = 4), A145838 (k = 5), A002407 (k = 6), A144974 (k = 7), A090562 (k = 10), A262344 (k = 11), A262493 (k = 13), A264821 (k = 14), A264822 (k = 15), A264823 (k = 16), A264824 (k = 17), A264825 (k = 18), A264844 (k = 19), A264845 (k = 20), A201715 (k = 24).

Intersection[Table[(21 k^2 + 21 k + 2)/2, {k, 0, 1000}], Prime[Range[33000]]]

lista(nn) = for(n=1, nn, if(isprime(p=(21*n^2 + 21*n + 2)/2), print1(p, ", "))); \\ Altug Alkan, Aug 26 2016

cp's OEIS Frontend

A201716 Primes of the form 3*m^2 - 4.

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A201717 Primes of the form 3*m^2 - 5.

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A201718 Primes of the form 3*m^2 - 7.

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A201781 Primes of the form 3*m^2 - 8.

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A276261 Centered 21-gonal primes.

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