A124181 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 is prime.

1, 3, 69, 86, 104, 110, 138, 146, 210, 238, 247, 260, 264, 269, 316, 436, 572, 600, 621, 654, 666, 715, 737, 740, 744, 754, 779, 1056, 1156, 1159, 1216, 1218, 1221, 1343, 1419, 1434, 1442, 1524, 1580, 1603, 1676, 1680, 1731, 1742, 1804, 1952, 1956, 1985

Offset: 1

Author

Artur Jasinski, Dec 13 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1390

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

Magma

[n: n in [0..2000] | IsPrime(s) where s is 1+&+[n^i: i in [1..23 by 2]]]; // Vincenzo Librandi, Jun 28 2014

Mathematica

Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23], Print[n]], {n, 1, 1400}]
Select[Range[3000], PrimeQ[Total[#^Range[1, 23, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)

PARI

is(n)=n==1 || isprime((n^25-n)/(n^2-1)+1) \\ Charles R Greathouse IV, Jul 02 2013

Sage

i,n = var('i,n')
[n for n in (1..2000) if is_prime(1+(n^(2*i+1)).sum(i,0,11))] # Bruno Berselli, Jun 27 2014

Formula

1 together with numbers n such that (n^25-n)/(n^2-1) + 1 is prime. - Charles R Greathouse IV, Jul 02 2013