A165682 -id:A165682 - cp's OEIS frontend

A165681 Primes p such that 3p(p-1)+1 is not prime.

13, 17, 19, 23, 37, 41, 47, 61, 71, 73, 79, 83, 97, 101, 103, 107, 113, 127, 131, 139, 149, 151, 163, 167, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 317, 331, 337, 349, 359, 367, 373, 379, 383, 397, 401

Offset: 1

Vincenzo Librandi, Sep 24 2009

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

Cf. A165682, A165683.

Select[Prime[Range[90]],!PrimeQ[3#(#-1)+1]&]  (* Harvey P. Dale, Mar 18 2011 *)

is(n)=isprime(n) && !isprime(3*n*(n-1)+1) \\ Charles R Greathouse IV, Feb 23 2017

A000040 \ A165682.

a(n) ~ n log n. - Charles R Greathouse IV, Feb 23 2017

2 and 3 removed by R. J. Mathar, Sep 26 2009

A165683 Primes of form 3p(p-1)+1 with p also a prime.

Original entry on oeis.org

7, 19, 61, 127, 331, 2437, 2791, 5419, 8269, 10267, 13267, 23497, 35317, 55897, 73477, 89269, 115837, 170647, 292969, 360187, 372769, 452797, 603457, 812761, 895987, 929077, 976411, 997057, 1074607, 1125469, 1253887, 1372957, 1609669, 1653919

Offset: 1

Vincenzo Librandi, Sep 24 2009

			a(3)= 61=3*5*(5-1)+1 generated by p=3. a(4)=127=3*7*(7-1)+1 generated by p=7. a(5)=331=3*11*(11-1)+1.

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

Cf. A165681, A165682.

[a: p in PrimesUpTo(1000) | IsPrime(a) where a is 3*p*(p-1)+1]; // Vincenzo Librandi, Sep 13 2013 *

Select[Table[3 p (p - 1) + 1, {p, Prime[Range[100]]}], PrimeQ] (* Vincenzo Librandi, Sep 13 2013 *)

a(n) = x^3-(x-1)^3 where x = A165682(n).

7 and 19 inserted by R. J. Mathar, Sep 26 2009

A171447 Numbers n such that n+1 is prime, and (n+1)^3-n^3 is prime.

Original entry on oeis.org

1, 2, 4, 6, 10, 28, 30, 42, 52, 58, 66, 88, 108, 136, 156, 172, 196, 238, 312, 346, 352, 388, 448, 520, 546, 556, 570, 576, 598, 612, 646, 676, 732, 742, 786, 856, 906, 940, 976, 1050, 1068, 1092, 1152, 1192, 1222, 1228, 1236, 1302, 1432, 1452, 1458, 1480

Offset: 1

Vincenzo Librandi, Dec 09 2009

			for n=10, 10+1=11 and 11^3-10^3=331; n=28, 28+1=29 and 29^3-28^3=2437

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

Cf. A165682.

[n: n in [1..1500] | IsPrime(n+1) and IsPrime( (n+1)^3-n^3)]; // Vincenzo Librandi, Apr 05 2013

Select[Range[1500], PrimeQ[# + 1]&&PrimeQ[(# + 1)^3 - #^3]&] (* Vincenzo Librandi, Apr 05 2013 *)

is(n)=isprime(n+1) && isprime(3*n^3+3*n+1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = A165682(n)-1. - R. J. Mathar, Jan 04 2011

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A165681 Primes p such that 3p(p-1)+1 is not prime.

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A165683 Primes of form 3p(p-1)+1 with p also a prime.

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A171447 Numbers n such that n+1 is prime, and (n+1)^3-n^3 is prime.

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cp's OEIS Frontend

A165681 Primes p such that 3*p*(p-1)+1 is not prime.

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Author

Keywords

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Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A165683 Primes of form 3*p*(p-1)+1 with p also a prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A171447 Numbers n such that n+1 is prime, and (n+1)^3-n^3 is prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A165681 Primes p such that 3p(p-1)+1 is not prime.

A165683 Primes of form 3p(p-1)+1 with p also a prime.