A228121 -id:A228121 - cp's OEIS frontend

A228353 Primes of the form 3p - 4 where p is prime.

2, 5, 11, 17, 29, 47, 53, 83, 89, 107, 137, 173, 179, 197, 233, 263, 317, 389, 443, 449, 467, 569, 587, 593, 677, 683, 719, 809, 827, 839, 929, 947, 1097, 1163, 1187, 1223, 1259, 1289, 1367, 1433, 1493, 1523, 1559, 1619, 1637, 1667, 1709, 1847, 1889, 1973, 1979

Offset: 1

Irina Gerasimova, Aug 20 2013

Subsequence of A003627. - Michel Marcus, May 30 2015

Paolo P. Lava, Table of n, a(n) for n = 1..300

Cf. A228121, A258261, A003627.

Select[3*Prime[Range[200]]-4, PrimeQ] (* Zak Seidov, May 24 2015 *)

is(n)=n%3==2 && isprime(n\3+2) && isprime(n) \\ Charles R Greathouse IV, Mar 18 2014

a(n) = 3*A258261(n)-4. Zak Seidov, May 24 2015

a(n) >> n*log^2 n. - _Charles R Greathouse IV, Jun 04 2015

A228358 Numbers n such that 3*n - 4 is not prime.

Original entry on oeis.org

1, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 23, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 49, 50, 52, 53, 54, 55, 56, 58, 60, 62, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 80, 82, 83, 84, 86, 88, 90, 92, 93, 94, 96, 97, 98, 100, 101

Offset: 1

Vincenzo Librandi, Aug 21 2013

After 1, all terms are given by A153170 +2. [Bruno Berselli, Aug 21 2013]

			8 is in the sequence since 3*8 - 4 = 20 is not prime.

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

Cf. A153170, A228121.

[n: n in [1..120] | not IsPrime(3*n -4)];

Mathematica
```
Select[Range[230], ! PrimeQ[3 # - 4]&]
```

A258261 Primes p such that 3p - 4 is also prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 29, 31, 37, 47, 59, 61, 67, 79, 89, 107, 131, 149, 151, 157, 191, 197, 199, 227, 229, 241, 271, 277, 281, 311, 317, 367, 389, 397, 409, 421, 431, 457, 479, 499, 509, 521, 541, 547, 557, 571, 617, 631, 659, 661, 677, 691, 701, 719

Offset: 1

Zak Seidov, May 24 2015

This sequence is interesting because of the comments in A258233: for n > 1, if 3 * prime(n) - 4 is prime then A258233(n) = 1 + A071704(n), otherwise A258233 (n) = A071704(n). - Zak Seidov, Jun 04 2015

Subsequence of primes of A228121. - Michel Marcus, May 30 2015

			3 * 2 - 4 = 2, 3 * 3 - 4 = 5, 3 * 5 - 4 = 11, 3 * 7 - 4 = 17, 3 * 11 - 4 = 29 are all prime, so 2, 3, 5, 7, 11 are all in the sequence.
3 * 13 - 4 = 35 = 5 * 7, so 13 is not in the sequence.

Cf. A023209 (3p + 4), A071704, A258233, A228353, A228121.

[p: p in PrimesUpTo(1000) | IsPrime(3*p-4)]; // Vincenzo Librandi, May 25 2015

Select[Prime[Range[200]], PrimeQ[3# - 4] &]

forprime(p=1,10^3,if(isprime(3*p-4),print1(p,", "))) \\ Derek Orr, May 27 2015

A247147 Numbers k such that 3*k-4 and 2^k-1 are prime.

Original entry on oeis.org

2, 3, 5, 7, 17, 19, 31, 61, 89, 107, 521, 1279, 9689, 9941, 21701, 23209, 216091, 13466917, 30402457, 57885161

Offset: 1

Vincenzo Librandi, Nov 21 2014

All terms are primes.

Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, arXiv:math/0404188 [math.NT], 2004-2007; Annals of Mathematics, 167 (2008), pp. 481-547.

Cf. A000043, A001348, A228121.

[n: n in [0..10000] | IsPrime(3*n-4) and IsPrime(2^n-1)];

Select[Range[10000], PrimeQ[2^# - 1] && PrimeQ[3 # - 4] &]

from sympy import isprime
from itertools import count, islice
def agen(startk=1):
    for k in count(startk):
        if isprime(3*k-4) and isprime(2**k-1):
            yield k
print(list(islice(agen(), 12))) # Michael S. Branicky, Jul 31 2022

a(20) using A000043 from Michael S. Branicky, Jul 31 2022

A268139 Semiprimes of the form 3n2^n - 3*n - 2^(2+n) + 4.

Original entry on oeis.org

6, 35, 341, 2159, 6160337, 27787211, 191126044583, 412745898649251217229, 162789115166027506149234835193, 51436190754860636195130229261336259

Offset: 1

Vincenzo Librandi, Jan 27 2016

nonn

Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Mathematics, 167 (2008), pp. 481-547. arXiv:math/0404188 [math.NT], 2004-2007.

Cf. A000043, A001348, A228121, A247147.

IsSemiprime:= func; [s: n in [2..240] | IsSemiprime(s) where s is 3*n*2^n-3*n-2^(2+n)+4];

Select[Table[3 n 2^n - 3 n - 2^(2 + n) + 4, {n, 250}], PrimeOmega[#] == 2 &]

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A228353 Primes of the form 3p - 4 where p is prime.

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A228358 Numbers n such that 3*n - 4 is not prime.

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A258261 Primes p such that 3p - 4 is also prime.

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A247147 Numbers k such that 3*k-4 and 2^k-1 are prime.

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A268139 Semiprimes of the form 3*n*2^n - 3*n - 2^(2+n) + 4.

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Magma

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A268139 Semiprimes of the form 3n2^n - 3*n - 2^(2+n) + 4.