A062324 -id:A062324 - cp's OEIS frontend

A244452 Primes p such that p^2-2 and p^2+4 are also prime (i.e., initial members of prime triples (p, p^2-2, p^2+4)).

3, 5, 7, 13, 37, 47, 103, 233, 293, 313, 607, 677, 743, 1367, 1447, 2087, 2543, 3023, 3803, 3863, 4093, 4153, 4373, 4583, 4643, 4793, 4957, 5087, 5153, 5623, 5683, 5923, 6287, 7177, 7247, 7547, 7817, 8093, 8527, 9133, 9403

Offset: 1

Felix Fröhlich, Jun 28 2014

nonn

Intersection of A062326 and A062324.

			3 is in the sequence since it is the first member of the triple (3, 3^2-2, 3^2+4) and the resulting values in the triple (3, 7, 13) are all prime.

Felix Fröhlich, Table of n, a(n) for n = 1..242507 (all terms up to 10^9)

Cf. A022004, A073648, A098413.

Select[Prime[Range[1200]],AllTrue[#^2+{4,-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 28 2018 *)

forprime(p=2, 10^4, if(isprime(p^2-2) && isprime(p^2+4), print1(p, ", ")))

A245048 Primes p such that p^2 + 28 is prime.

Original entry on oeis.org

3, 5, 11, 13, 17, 19, 23, 41, 43, 47, 53, 67, 79, 83, 89, 97, 109, 131, 137, 149, 157, 163, 167, 179, 181, 193, 211, 223, 239, 241, 251, 263, 277, 281, 311, 317, 331, 379, 397, 401, 409, 421, 431, 439, 443, 449, 457, 467, 479, 541, 569, 599, 643, 647, 673

Offset: 1

Chai Wah Wu, Jul 10 2014

nonn

7 of the first 8 odd primes are in this list.

			3 is in the sequence because 3^2 + 28 = 37, which is also prime.
5 is in the sequence because 5^2 + 28 = 53, which is also prime.
7 is not in the sequence because 7^2 + 28 = 77 = 7 * 11.

Chai Wah Wu, Table of n, a(n) for n = 1..2000

Cf. A062324 (p^2+4), A062718(p^2+6), A243367(p^2+10).

A245048:=n->`if`(isprime(n) and isprime(n^2+28), n, NULL): seq(A245048(n), n=1..10^3); # Wesley Ivan Hurt, Jul 24 2014

Select[Prime[Range[200]], PrimeQ[#^2 + 28] &] (* Alonso del Arte, Jul 12 2014 *)

import sympy
[sympy.prime(n) for n in range(1,10**6) if sympy.ntheory.isprime(sympy.prime(n)**2+28)]

A129119 Numbers of the form 2*p (with p a prime number) such that p^2+4 is prime.

Original entry on oeis.org

6, 10, 14, 26, 34, 74, 94, 134, 146, 194, 206, 274, 326, 334, 386, 466, 554, 586, 614, 626, 634, 694, 746, 926, 974, 1006, 1094, 1154, 1186, 1214, 1226, 1354, 1486, 1574, 1646, 1654, 1706, 1766, 1906, 1934, 1966, 1994, 2174, 2234, 2246, 2474, 2734, 2846

Offset: 1

Giovanni Teofilatto, May 25 2007

			7^2 + 4 = 53 which is a prime number. Therefore 2*7 is in the sequence.

Cf. A045637, A062324.

2*Select[Prime@Range[250], PrimeQ[ #^2 + 4] &] (* Ray Chandler, May 27 2007 *)
a={};For[n=1,n<300,n++,If[PrimeQ[Prime[n]^2 + 4], AppendTo[a, 2*Prime[n]]]]; a (* Stefan Steinerberger, May 27 2007 *)

a(n) = 2*A062324(n).

Extended and edited by Ray Chandler and Stefan Steinerberger, May 27 2007

A347530 Primes of the form (p^2 + 9)/2 where p is prime.

Original entry on oeis.org

17, 29, 89, 149, 269, 929, 1109, 1409, 3449, 5309, 6389, 8069, 12329, 14969, 33029, 34589, 42929, 47129, 48989, 60209, 67349, 78809, 98129, 109049, 118589, 136769, 158489, 175829, 213209, 264269, 317609, 338669, 363809, 367229, 389849, 438989, 454109, 467549

Offset: 1

Burak Muslu, Sep 05 2021

nonn

Each p is an odd number, so p^2 == 1 (mod 8), thus (p^2 + 9)/2 == 1 (mod 4).

			17 is in the sequence as 17 = (p^2 + 9)/2 where p = 5 is prime.
29 is in the sequence as 29 = (p^2 + 9)/2 where p = 7 is prime.

Cf. A000040, A045637, A062324.

Subsequence of A076727 and of A103739.

Select[(Select[Range[3, 1000], PrimeQ]^2 + 9)/2, PrimeQ] (* Amiram Eldar, Sep 05 2021 *)

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A244452 Primes p such that p^2-2 and p^2+4 are also prime (i.e., initial members of prime triples (p, p^2-2, p^2+4)).

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A245048 Primes p such that p^2 + 28 is prime.

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A129119 Numbers of the form 2*p (with p a prime number) such that p^2+4 is prime.

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A347530 Primes of the form (p^2 + 9)/2 where p is prime.

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