A124178 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.

1, 3, 6, 33, 36, 61, 70, 99, 168, 229, 267, 268, 321, 325, 337, 366, 387, 448, 456, 457, 498, 513, 532, 546, 591, 621, 624, 637, 835, 858, 910, 927, 961, 981, 1045, 1125, 1213, 1237, 1242, 1257, 1341, 1357, 1437, 1458, 1461, 1462, 1482, 1491, 1572, 1579, 1581

Offset: 1

Author

Artur Jasinski, Dec 13 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1800

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

Magma

[n: n in [0..2000] | IsPrime(1 +n +n^3 +n^5 +n^7 +n^9 +n^11 +n^13 +n^15 +n^17 +n^19)]; // Vincenzo Librandi, Nov 12 2010

Magma

[n: n in [0..2000] | IsPrime(s) where s is 1+&+[n^i: i in [1..19 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], Print[n]], {n, 1, 1000}]
Select[Range[3000], PrimeQ[Total[#^Range[1, 19, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)

PARI

is(n)=n==1 || isprime((n^21-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,0,9))] # Bruno Berselli, Jun 28 2014