A171748 -id:A171748 - cp's OEIS frontend

A171749 Odd primes of the form (1+n)(2+2n)+n(3+2n) = 4n^2+7n+2.

13, 59, 137, 389, 563, 769, 1277, 1579, 1913, 2677, 5147, 5737, 6359, 7013, 7699, 9949, 12487, 13397, 15313, 16319, 18427, 20663, 23027, 26813, 32309, 36767, 38317, 41513, 43159, 51869, 61379, 63377, 65407, 73847, 78259, 80513, 82799, 89849

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 17 2009

This sequence is infinite under the Bunyakovsky conjecture. - Charles R Greathouse IV, Apr 04 2012

Also primes of the form 16*m^2-2*m-1, by the substitution n=2*m-1. [Note that n is odd because otherwise 4n^2+7n+2 is even]. - Bruno Berselli, Jul 03 2012

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

Cf. A171748.

f[n_] := (1+n)(2+2*n)+n*(3+2*n); lst={}; Do[If[PrimeQ[f[n]], AppendTo[lst, f[n]]], {n, 6!}]; lst
Select[Table[4*n^2+7*n+2,{n, 1000}],PrimeQ] (* Vincenzo Librandi, Aug 01 2012 *)

A171838 Primes of the form 3k^2 + 9k + 5.

Original entry on oeis.org

5, 17, 59, 89, 167, 269, 467, 719, 1259, 1949, 2267, 2609, 2789, 3167, 3779, 4217, 4679, 4919, 5417, 5939, 7349, 7649, 9239, 10979, 11717, 12479, 14489, 15767, 16649, 17099, 18959, 21419, 21929, 24029, 25667, 28517, 31517, 34667, 35969, 36629

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 19 2009

Primes of the form 12*k^2 + 18*k + 5. - Charles R Greathouse IV, Apr 13 2012

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Cf. A171748, A171749.

[3*n^2 +9*n +5: n in [0..250] | IsPrime(3*n^2 +9*n +5)]; // G. C. Greubel, Apr 29 2021

Select[Table[3n^2+9n+5, {n,0,200}], PrimeQ] (* Harvey P. Dale, Jul 18 2014 *)

for(n=0,99,if(isprime(t=12*n^2+18*n+5),print1(t", "))) \\ Charles R Greathouse IV, Apr 13 2012

[3*n^2 +9*n +5 for n in (0..250) if is_prime(3*n^2 +9*n +5)] # G. C. Greubel, Apr 29 2021

Definition simplified by Charles R Greathouse IV, Apr 13 2012

A182048 Numbers n such that 16n^2-2n-1 and 16n^2+2n-1 are both primes.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 13, 19, 29, 32, 36, 62, 63, 70, 75, 78, 85, 93, 96, 102, 107, 109, 119, 123, 128, 145, 158, 164, 174, 177, 190, 192, 197, 219, 241, 247, 252, 280, 284, 299, 304, 318, 335, 340, 344, 354, 361, 374, 377, 382, 385, 387, 427, 434, 439, 440

Offset: 1

Gerasimov Sergey, Apr 08 2012

nonn

			a(1)=1 because 16*1^2-2*1-1=13 is prime and 16*1^2+2*1-1=17 is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..3500

Cf. A171748, A089637.

Select[Range[500], PrimeQ[16 #^2 - 2 # - 1] && PrimeQ[16 #^2 + 2 # - 1] &] (* T. D. Noe, Apr 16 2012 *)
Select[Range[500],AllTrue[16#^2-1+{2#,-2#},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 01 2018 *)

Corrected and extended by T. D. Noe, Apr 16 2012

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A171749 Odd primes of the form (1+n)(2+2n)+n(3+2n) = 4n^2+7n+2.

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A171838 Primes of the form 3k^2 + 9k + 5.

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A182048 Numbers n such that 16n^2-2n-1 and 16n^2+2n-1 are both primes.

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cp's OEIS Frontend

A171749 Odd primes of the form (1+n)*(2+2*n)+n*(3+2*n) = 4*n^2+7*n+2.

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Author

Keywords

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Programs

Mathematica

A171838 Primes of the form 3*k^2 + 9*k + 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Extensions

A182048 Numbers n such that 16n^2-2n-1 and 16n^2+2n-1 are both primes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A171749 Odd primes of the form (1+n)(2+2n)+n(3+2n) = 4n^2+7n+2.

A171838 Primes of the form 3k^2 + 9k + 5.