A023213 -id:A023213 - cp's OEIS frontend

A163182 Primes p such that neither 4p+3 nor 4p-3 are prime.

3, 13, 43, 53, 73, 83, 97, 127, 137, 139, 163, 167, 173, 197, 199, 211, 223, 251, 269, 277, 281, 293, 311, 317, 337, 347, 379, 383, 397, 409, 419, 421, 433, 443, 449, 463, 491, 503, 547, 557, 563, 593, 601, 607, 613, 617, 641, 643, 727, 733, 757, 787, 809

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 22 2009

Primes neither in A023213 nor in A157978.

			For p=3, 4*3+3=15 (not prime) and 4*3-3=9 (not prime), so the prime p=3 is in the sequence.
For p=7, 4*7+3=31 (prime), so the prime p=7 is not in the sequence.

Marius A. Burtea, Table of n, a(n) for n = 1..5673

Cf. A023213, A106015, A157978.

lst={};Do[p=Prime[n];If[ !PrimeQ[2*p+(p-1)+(p-2)]&&!PrimeQ[2*p+(p+1)+(p+2)], AppendTo[lst,p]],{n,3*5!}];lst
Select[Prime[Range[150]],NoneTrue[4#+{3,-3},PrimeQ]&] (* Harvey P. Dale, Aug 01 2022 *)

isok(p) = isprime(p) && !isprime(4*p+3) && !isprime(4*p-3); \\ Michel Marcus, Oct 12 2018

Edited by R. J. Mathar, Jul 25 2009, Jul 27 2009

A238699 Primes p such that 2p + 3 and 4p + 3 are both prime.

Original entry on oeis.org

2, 5, 7, 17, 19, 47, 67, 89, 157, 227, 229, 307, 349, 439, 467, 487, 509, 599, 647, 797, 929, 1039, 1187, 1217, 1237, 1259, 1307, 1427, 1447, 1567, 1789, 2027, 2309, 2467, 2539, 2707, 2789, 2819, 3167, 3457, 3499, 3659, 3877, 3919, 4057, 4079, 4157, 4289, 4297

Offset: 1

Ilya Lopatin, Mar 03 2014, following a suggestion by Juri-Stepan Gerasimov

nonn

Intersection of A023204 and A023213.

Primes in A115334.

			89 is in the sequence because 2*89 + 3 = 181 and 4*89 + 3 = 359 are both prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A023204, A023213; A115334.

[p: p in PrimesUpTo(4500) | IsPrime(2*p+3) and IsPrime(4*p+3)]; // Bruno Berselli, Mar 03 2014

Select[Prime[Range[600]],AllTrue[{2#+3,4#+3},PrimeQ]&] (* Harvey P. Dale, Dec 24 2023 *)

select(p->isprime(2*p+3)&&isprime(4*p+3), primes(1000)) \\ Charles R Greathouse IV, Mar 06 2014

Edited by Bruno Berselli, Mar 03 2014

A372113 Numbers k for which (k-1)/2 and 2*k+1 are both primes.

Original entry on oeis.org

5, 11, 15, 23, 35, 39, 63, 75, 83, 95, 119, 135, 179, 215, 219, 299, 303, 315, 359, 363, 455, 459, 483, 515, 543, 615, 663, 699, 719, 735, 779, 803, 879, 915, 923, 935, 975, 999, 1019, 1043, 1143, 1155, 1175, 1199, 1295, 1323, 1355, 1383, 1439, 1539, 1595, 1659, 1679, 1755, 1763, 1815, 1859, 1883

Offset: 1

Alexandre Herrera, Apr 19 2024

nonn

Intersection of A072055 and A104635.

			5 is a term because (5-1)/2 = 2 is prime and 2*5+1 = 11 is prime.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A072055, A104635.

Cf. A023213, A126330.

Select[Range[1, 2000, 2], AllTrue[{(# - 1)/2, 2 # + 1}, PrimeQ] &] (* Michael De Vlieger, Apr 19 2024 *)

from sympy import isprime
def a(n): return n%2 == 1 and isprime((n-1)>>1) and isprime(2*n+1)
print([n for n in range(2, 1900) if a(n)])

a(n) = 2*A023213(n) + 1.

a(n) = (A126330(n)-1)/2.

cp's OEIS Frontend

A163182 Primes p such that neither 4p+3 nor 4p-3 are prime.

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A238699 Primes p such that 2p + 3 and 4p + 3 are both prime.

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Author

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Magma

Mathematica

PARI

Extensions

A372113 Numbers k for which (k-1)/2 and 2*k+1 are both primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Formula