A124209 Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^61 + n^63 is prime.

5, 15, 140, 359, 615, 876, 941, 1109, 1230, 1292, 1302, 1325, 1752, 1799, 2064, 2535, 2645, 2690, 2942, 3042, 3138, 3200, 3449, 3473, 3527, 3560, 3713, 4070, 4488, 4658, 4767, 5055, 5169, 5195, 5472, 5592, 5604, 5841, 5856, 5939, 6201, 6669, 6677, 6731, 6857

Offset: 1

Author

Artur Jasinski, Dec 13 2006

Keywords

• nonn
• easy

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1237 (n = 1..230 from Vincenzo Librandi)

Crossrefs

Cf. A049407, similar sequences listed in A244376.

Programs

Magma

[n: n in [0..5000] | IsPrime(s) where s is 1+&+[n^i: i in [1..63 by 2]]]; // Vincenzo Librandi, Jun 28 2014

Maple

a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 1, a(n-1)) while
        not isprime(1+(k^65-k)/(k^2-1)) do od; k
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jun 26 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 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43 + n^45 + n^47 + n^49 + n^51 + n^53 + n^55 + n^57 + n^59 + n^61 + n^63],Print[n]],{n,1,2400}]
Select[Range[7000], PrimeQ[Total[#^Range[1, 63, 2]] + 1] &] (* Vincenzo Librandi, Jun 28 2014 *)

PARI

for(n=1,10^4,if(ispseudoprime(sum(i=0,31,n^(2*i+1))+1),print1(n,", "))) \\ Derek Orr, Jun 24 2014

Extensions

a(28) and beyond from Derek Orr, Jun 24 2014