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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.
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%I #28 Mar 01 2020 05:41:49

%S 184279409,619338131,913749803,1057351301,1507289869,1600204213,

%T 2845213937,4725908767,4760956439,5374709801,5518707641,8724256757,

%U 9044067313,9387396269,10992352517,11937043567,13493126359,13593105793,17891702891,17897035213,17954907767,19690938161,20227580927,20922685813,21313027583,21717176851

%N 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.

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

%C No terms < 10^11 with (p^12 + 5)/6 prime. - _Chai Wah Wu_, Jan 27 2015

%H Chai Wah Wu, <a href="/A253941/b253941.txt">Table of n, a(n) for n = 1..67</a>

%o (Python)

%o from gmpy2 import is_prime, t_divmod

%o A253941_list = []

%o for p in range(1,10**6,2):

%o ....if is_prime(p):

%o ........p2, x = p**2, 1

%o ........for i in range(5):

%o ............x *= p2

%o ............q, r = t_divmod(x+5,6)

%o ............if r or not is_prime(q):

%o ................break

%o ........else:

%o ............A253941_list.append(p) # _Chai Wah Wu_, Jan 22 2015

%o (PARI) 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

%Y Subsequence of A253976.

%Y Cf. A118915, A247478, A253925, A253940.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 20 2015

%E a(15)-a(26) from _Chai Wah Wu_, Jan 22 2015