A123099 - OEIS

%I #15 Oct 29 2022 13:41:06

%S 547,35983,111049,2738179,6076687,15860209,53530639,685318537,

%T 1043755441,1670649571,2347515619,9761226721,10330521727,12188475769,

%U 15042514033,25486958659,30383211043,40608270601,45701408383

%N Primes of the form 1 + 2n + 3n^2 + 4n^3 + 5n^4.

%C Quintic analog of A123059 Primes of the form 1+2n+3n^2+4n^3 = primes in A056578. Corresponding values of n are 3, 9, 12, 27, 33, 42, 57, 108, 120, 135, 147. One must have 3|n else 3|quintic. Note that 1+2n+3n^2+4n^3+5n^4 is the derivative of 1+n+n^2+n^3+n^4+n^5 = A053700.

%H Harvey P. Dale, <a href="/A123099/b123099.txt">Table of n, a(n) for n = 1..1000</a>

%F A000040 INTERSECTION {1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 for n>0}. Primes in A056579.

%t Select[Table[1+2n+3n^2+4n^3+5n^4,{n,500}],PrimeQ] (* _Harvey P. Dale_, Oct 29 2022 *)

%o (Magma) [ a: n in [0..400] | IsPrime(a) where a is 1+2*n+3*n^2+4*n^3+5*n^4] // _Vincenzo Librandi_, Nov 13 2010

%Y Cf. A000040, A000012, A005408, A053699, A053700, A056109, A056579, A056578, A113531, A113532, A113618, A113630, A113632, A123059.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 27 2006