A265121 -id:A265121 - cp's OEIS frontend

A267030 Primes p such that p*(3^p) + 2 is also prime.

3, 5, 11, 17, 317, 373, 10313

Offset: 1

Emre APARI, Jan 09 2016

The terms of this sequence are the prime terms of A265121.
The first few corresponding primes are 83, 1217, 1948619, 2195382773, ... .
a(8) > 10^5. - Michael S. Branicky, Oct 08 2024

			p = 17; [17 * (3 ^ 17) + 2] = 2195382773 (is a prime number).

Cf. A265121.

[p: p in PrimesUpTo(1000) | IsPrime((p*(3^p)+2))]; // Vincenzo Librandi, Jan 10 2016

select(p -> isprime(p) and isprime(p*3^p+2), [seq(i,i=3..2000,2)]); # Robert Israel, Jan 10 2016

Select[Prime@ Range@ 1000, PrimeQ[# (3^#) + 2] &] (* Michael De Vlieger, Jan 09 2016 *)

lista(nn) = forprime(p=2, nn, if(ispseudoprime((p*(3^p) + 2)), print1(p, ", "))); \\ Altug Alkan, Jan 10 2016

A382094 Integers k such that k*2^k + 3 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 10, 11, 28, 40, 110, 124, 826, 871, 1355, 1540, 2285, 8908, 20824, 31715, 61655, 75920, 96274, 195871, 233125, 242594, 252760, 259825, 349315

Offset: 1

Juri-Stepan Gerasimov, Mar 15 2025

			4 is in the sequence because 4*2^4 + 3 = 67 is prime.

Cf. A182373, A182375, A265121.

Magma
```
[k: k in [0..1000] | IsPrime(k*2^k+3)];
```

Select[Range[0,5000],PrimeQ[#*2^#+3] &] (* Stefano Spezia, Mar 15 2025 *)

a(18)-a(22) from Michael S. Branicky, Mar 15 2025
a(23)-a(25) from Georg Grasegger, Apr 15 2025
a(26)-a(28) from Georg Grasegger, May 14 2025

cp's OEIS Frontend

A267030 Primes p such that p*(3^p) + 2 is also prime.

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