A123099 Primes of the form 1 + 2n + 3n^2 + 4n^3 + 5n^4.

547, 35983, 111049, 2738179, 6076687, 15860209, 53530639, 685318537, 1043755441, 1670649571, 2347515619, 9761226721, 10330521727, 12188475769, 15042514033, 25486958659, 30383211043, 40608270601, 45701408383

Offset

1,1

Comments

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A176089 A261112 A219082 * A263524 A300899 A253546

Adjacent sequences: A123096 A123097 A123098 * A123100 A123101 A123102

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 27 2006

Status

approved