A045371 -id:A045371 - cp's OEIS frontend

A153502 Primes of the form 3n^2 - 3n + 11.

11, 17, 29, 47, 71, 101, 137, 179, 227, 281, 479, 557, 641, 827, 929, 1151, 1667, 1811, 2447, 2621, 2801, 3581, 4007, 4229, 4457, 4691, 4931, 6221, 6779, 8597, 9587, 9929, 10631, 12107, 12491, 13679, 14087, 16217, 16661, 19937, 25127, 25679, 26237

Offset: 1

Vincenzo Librandi, Dec 28 2008

Subsequence of A003627, A007528, A045371. - Bruno Berselli, Jul 16 2012

Also primes p such that (4*p-41)/3 is a square. - Bruno Berselli, Sep 14 2015

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

Cf. A003627, A007528, A045371.

[a: n in [1..100] | IsPrime(a) where a is 3*n^2-3*n+11]; // Vincenzo Librandi, Jul 16 2012

Select[Table[3 n^2 - 3 n + 11, {n, 1, 700}], PrimeQ] (* Vincenzo Librandi, Jul 16 2012 *)

lista(nn) = for (n=1, nn, if (isprime(p=3*n^2-3*n+11), print1(p, ", "))) \\ Michel Marcus, Sep 14 2015

A241013 Semiprimes congruent to {1, 2, 4} mod 5.

Original entry on oeis.org

4, 6, 9, 14, 21, 22, 26, 34, 39, 46, 49, 51, 57, 62, 69, 74, 77, 82, 86, 87, 91, 94, 106, 111, 119, 121, 122, 129, 134, 141, 142, 146, 159, 161, 166, 169, 177, 187, 194, 201, 202, 206, 209, 214, 217, 219, 221, 226, 237, 247, 249, 254, 259, 262, 267, 274, 287, 289

Offset: 1

K. D. Bajpai, Aug 07 2014

Semiprimes in A032793.

			21 = 3 * 7 which is semiprime and 21 = 1 mod 5.
39 = 3 * 13 which is semiprime and 39 = 4 mod 5.

K. D. Bajpai, Table of n, a(n) for n = 1..11280

Cf. A001358, A032793, A045371.

Select[Range[500], PrimeOmega[#] == 2 && MemberQ[{1, 2, 4}, Mod[#, 5]] &](* Bajpai *)
Select[Complement[Range[100], 5Range[20] - 2, 5Range[20]], PrimeOmega[#] == 2 &] (* Alonso del Arte, Aug 07 2014 *)

for(n=1,10^4,if(n!=Mod(0,5)&&n!=Mod(3,5),if(bigomega(n)==2,print1(n,", ")))) \\ Derek Orr, Aug 07 2014

A269788 Primes p such that 2*p + 47 is a square.

Original entry on oeis.org

17, 37, 61, 89, 157, 197, 241, 397, 457, 521, 661, 1277, 1381, 1489, 1601, 2089, 2221, 2357, 2789, 3257, 3761, 4877, 5077, 5281, 5701, 6361, 7057, 7297, 7541, 7789, 8297, 8821, 10781, 11681, 12301, 13921, 15289, 15641, 17837, 18217, 19381, 19777, 20177, 21401

Offset: 1

Vincenzo Librandi, Mar 24 2016

nonn

Primes of the form 2*k^2 + 2*k - 23.

Cf. A000040.
Subsequence of A002144, A045371.
Cf. similar sequences listed in A269784.

[p: p in PrimesUpTo(50000) | IsSquare(2*p+47)];

Select[Prime[Range[2500]], IntegerQ[Sqrt[2 # + 47]] &]

lista(nn) = {forprime(p=2, nn, if(issquare(2*p + 47), print1(p, ", "))); } \\ Altug Alkan, Mar 24 2016

a(1) = 17 because 2*17 + 47 = 81, which is a square.

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A153502 Primes of the form 3n^2 - 3n + 11.

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A241013 Semiprimes congruent to {1, 2, 4} mod 5.

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A269788 Primes p such that 2*p + 47 is a square.

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cp's OEIS Frontend

A153502 Primes of the form 3*n^2 - 3*n + 11.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A241013 Semiprimes congruent to {1, 2, 4} mod 5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A269788 Primes p such that 2*p + 47 is a square.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A153502 Primes of the form 3n^2 - 3n + 11.