A253976 -id:A253976 - cp's OEIS frontend

A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.

184279409, 619338131, 913749803, 1057351301, 1507289869, 1600204213, 2845213937, 4725908767, 4760956439, 5374709801, 5518707641, 8724256757, 9044067313, 9387396269, 10992352517, 11937043567, 13493126359, 13593105793, 17891702891, 17897035213, 17954907767, 19690938161, 20227580927, 20922685813, 21313027583, 21717176851

Offset: 1

Zak Seidov, Jan 20 2015

nonn

The sequence contains all terms up to 10^10. There are no terms as yet for which (p^12 + 5)/6 is also prime.

No terms < 10^11 with (p^12 + 5)/6 prime. - Chai Wah Wu, Jan 27 2015

Chai Wah Wu, Table of n, a(n) for n = 1..67

Subsequence of A253976.

Cf. A118915, A247478, A253925, A253940.

lista(nn) = forprime(p=5, nn, if(ispseudoprime((p^2 + 5)/6) && ispseudoprime((p^4 + 5)/6) && ispseudoprime((p^6 + 5)/6) && ispseudoprime((p^8 + 5)/6) && ispseudoprime((p^10 + 5)/6), print1(p, ", "))); \\ Jinyuan Wang, Mar 01 2020

from gmpy2 import is_prime, t_divmod
A253941_list = []
for p in range(1,10**6,2):
    if is_prime(p):
        p2, x = p**2, 1
        for i in range(5):
            x *= p2
            q, r = t_divmod(x+5,6)
            if r or not is_prime(q):
                break
        else:
            A253941_list.append(p) # Chai Wah Wu, Jan 22 2015

a(15)-a(26) from Chai Wah Wu, Jan 22 2015

A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

Original entry on oeis.org

524521, 1090891, 1383391, 2633509, 3371059, 4872331, 7304131, 7756669, 8819119, 8877331, 11536471, 12290851, 13362211, 13509649, 14658499, 15359401, 17094151, 17582329, 18191179, 18550891, 19416259, 20465209, 21971629, 22519531, 22619431, 25972561, 27155881, 29281699

Offset: 1

K. D. Bajpai, Jan 23 2015

nonn

All the terms in this sequence are 1 mod 9.

			a(1) = 524521;
(524521^3 + 2)/3 = 48102471044890921;
(524521^5 + 2)/3 = 13234061480615091039311002201;
(524521^7 + 2)/3 = 3640985160809159281478976663465873196681;
all four are prime.

K. D. Bajpai, Table of n, a(n) for n = 1..733

Cf. A241120, A253941, A253976, A253940.

[p: p in PrimesInInterval(3, 10000000) | IsPrime((p^3 + 2) div 3) and IsPrime((p^5 + 2) div 3) and IsPrime((p^7 + 2) div 3)]; // Vincenzo Librandi, Mar 27 2015

Select[Prime[Range[10^7]], PrimeQ[(#^3 + 2)/3] && PrimeQ[(#^5 + 2)/3] && PrimeQ[(#^7 + 2)/3] &]

is(n)=n%9==1 && isprime(n) && isprime((n^3+2)/3) && isprime((n^5+2)/3) && isprime((n^7+2)/3) \\ Charles R Greathouse IV, Jan 23 2015

A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

Original entry on oeis.org

37, 521, 881, 1619, 2053, 2213, 2341, 3527, 3637, 3727, 4157, 5147, 7019, 10009, 10891, 12277, 14741, 15913, 16273, 17747, 18757, 24499, 25307, 25577, 26209, 27073, 31481, 31517, 32833, 35083, 36739, 36791, 39079, 40231, 40949, 41039, 42013, 42461, 42767, 47917

Offset: 1

K. D. Bajpai, Apr 15 2015

			a(1) = 37; (37^2 + 2)/3 = 457; (37^4 + 2)/3 = 624721; all three are prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A241120, A253941, A253976, A253940.

[p: p in PrimesUpTo(5*10^4) | IsPrime((p^2+2) div 3)  and IsPrime((p^4+2) div 3 )]; // Vincenzo Librandi, Apr 20 2015

Select[Prime[Range[10^4]], PrimeQ[(#^2 + 2)/3] && PrimeQ[(#^4 + 2)/3] &]

forprime(p=1,10^5,if(!((p^2+2)%3)&&!((p^4+2)%3)&&isprime((p^2+2)/3)&&isprime((p^4+2)/3),print1(p,", "))) \\ Derek Orr, Apr 16 2015

cp's OEIS Frontend

A253941 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, (p^6 + 5)/6, (p^8 + 5)/6 and (p^10 + 5)/6 are all prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python

Extensions

A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI