A239925 Integers n such that 2n^2+1, 2n^3+1, 2n^4+1 and 2n^5+1 are prime.

1, 30, 8025, 44250, 49335, 49599, 155061, 218196, 255975, 293754, 324684, 333405, 336045, 367839, 381804, 416796, 476814, 514005, 529650, 558291, 668856, 682716, 747810, 893190, 930336, 933576, 1004004, 1246266, 1270860, 1383126, 1392111, 1427211, 1491645, 1497024, 1745904, 1786551

Offset: 1

Author

Zak Seidov, Mar 29 2014

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..134

Crossrefs

Subsequence of A239920. Cf. A089001, A168550, A239874.

Programs

Mathematica

Select[Range[0, 2000000], PrimeQ[2 #^2 + 1] && PrimeQ[2 #^3 + 1] && PrimeQ[2 #^4 + 1] && PrimeQ[2 #^5 + 1] &] (* Vincenzo Librandi, Mar 29 2014 *)
Select[Range[179*10^4], AllTrue[2 #^Range[2, 5] + 1, PrimeQ] &] (* Harvey P. Dale, Sep 24 2021 *)

PARI

s=[]; for(n=1, 2000000, if(isprime(2*n^2+1) && isprime(2*n^3+1) && isprime(2*n^4+1) && isprime(2*n^5+1), s=concat(s, n))); s \\ Colin Barker, Mar 29 2014