A243595 -id:A243595 - cp's OEIS frontend

A243630 Primes p such that 2*p^3 - 3 is also prime.

2, 7, 11, 13, 47, 101, 107, 151, 163, 167, 251, 257, 401, 443, 467, 521, 571, 641, 653, 673, 797, 907, 911, 971, 983, 997, 1013, 1151, 1153, 1181, 1187, 1223, 1231, 1277, 1291, 1303, 1361, 1433, 1481, 1511, 1597, 1637, 1723, 1741, 1811, 1951, 2027, 2081, 2083, 2141, 2287, 2311

Offset: 1

Vincenzo Librandi, Jun 08 2014

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

Cf. A063908, A023204, A153507, A174363, A243595.

[p: p in PrimesUpTo(2500) | IsPrime(2*p^3 - 3)];

Select[Prime[Range[2500]], PrimeQ[2 #^3 - 3] &]

A356510 Primes p such that 2p^2 - 7, 2p^2 - 1, and 2*p^2 + 3 are prime.

Original entry on oeis.org

43, 127, 197, 3613, 3767, 4957, 28687, 29723, 40193, 46817, 66403, 78737, 89137, 93253, 104243, 105337, 105673, 110543, 114113, 123397, 127247, 145963, 148303, 168713, 173293, 190387, 201893, 207367, 213613, 241597, 256117, 261323, 268253, 278543, 283807, 333227, 339373, 340913, 356173, 359143

Offset: 1

J. M. Bergot and Robert Israel, Aug 09 2022

nonn

All terms == 3 or 7 (mod 10).

All terms == 1 or 13 (mod 14). - Jon E. Schoenfield, Sep 05 2022

			a(3) = 197 is a term because 197, 2*197^2 - 7 = 77611, 2*197^2 - 1 = 77617, and 2*197^2 + 3 = 77621 are all prime.

Robert Israel, Table of n, a(n) for n = 1..1000

Contained in A106483 and A243595.

filter:= p -> isprime(p) and isprime(2*p^2+3) and isprime(2*p^2-1) and isprime(2*p^2-7):
select(filter, [seq(i,i=3..1000000,2)]);

Select[Prime[Range[30000]], AllTrue[2*#^2 + {-7, -1, 3}, PrimeQ] &] (* Amiram Eldar, Aug 09 2022 *)

from sympy import isprime
def ok(n): return isprime(n) and all(isprime(2*n*n-i) for i in [7, 1, -3])
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Aug 09 2022

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A243630 Primes p such that 2*p^3 - 3 is also prime.

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A356510 Primes p such that 2p^2 - 7, 2p^2 - 1, and 2*p^2 + 3 are prime.

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cp's OEIS Frontend

A243630 Primes p such that 2*p^3 - 3 is also prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

A356510 Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

A356510 Primes p such that 2p^2 - 7, 2p^2 - 1, and 2*p^2 + 3 are prime.