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

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

Author

K. D. Bajpai, Jan 23 2015

Keywords

• nonn

Comments

All the terms in this sequence are 1 mod 9.

Examples

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

Links

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

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Programs

Magma

[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

Mathematica

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

PARI

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