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

1,1

Comments

All the terms in this sequence are 1 mod 9.

Links

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Sequence in context: A017701 A013967 A036097 * A170802 A092018 A203930

Adjacent sequences: A254036 A254037 A254038 * A254040 A254041 A254042

Keyword

nonn

Author

K. D. Bajpai, Jan 23 2015

Status

approved