A244376 Numbers k such that 1 + k + k^3 + k^5 + k^7 + k^9 + k^11 is prime.

1, 2, 10, 40, 47, 55, 62, 121, 137, 152, 167, 201, 233, 278, 290, 293, 313, 333, 370, 382, 430, 452, 460, 506, 546, 555, 613, 625, 642, 675, 705, 711, 752, 767, 793, 797, 831, 835, 837, 872, 878, 891, 906, 917, 923, 978, 985, 1005, 1012, 1017, 1018, 1021

Offset: 1

Author

Vincenzo Librandi, Jun 27 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1400

Crossrefs

Cf. A127936.

Cf. numbers n such that 1+n+n^3 + ... + n^k, with k odd: A006093 (k=1), A049407 (k=3), A124154 (k=5), A124150 (k=7), A124163 (k=9), this sequence (k=11), A124164 (k=13), A244377 (k=15), A244378 (k=17), A124178 (k=19), A244379 (k=21), A124181 (k=23), A244380 (k=25), A124185 (k=27), A244383 (k=29), A124186 (k=31), A244384 (k=33), A124187 (k=35), A244385 (k=37), A124189 (k=39), A244386 (k=41), A124200 (k=43), A244387 (k=45), A124205 (k=47), A244388 (k=49), A124206 (k=51), A244389 (k=53), A124207 (k=55), A244390 (k=57), A124208 (k=59), A244391 (k=61), A124209 (k=63).

Programs

Magma

[n: n in [0..1500] | IsPrime(s) where s is 1+&+[n^i: i in [1..11 by 2]]];

Mathematica

Select[Range[4000], PrimeQ[Total[#^Range[1, 11, 2]] + 1] &]

PARI

isok(n) = isprime(1 + n + n^3 + n^5 + n^7 + n^9 + n^11); \\ Michel Marcus, Jun 27 2014

Sage

i,n = var('i,n')
[n for n in (1..2000) if is_prime(1+(n^(2*i+1)).sum(i,0,5))] # Bruno Berselli, Jun 27 2014