[seqfan] am asking for help by someone who wants to program in in Mathematica, or MAPLE, or whatever

Jonathan Post jvospost3 at gmail.com
Tue Nov 13 23:45:54 CET 2012

```I am intending to create a new seq, but tried n=1 through 80 without
finding a single value that met the definition.  So I am asking for
help by someone who wants to program in in Mathematica, or MAPLE, or
whatever.

Numbers n such that n^1+n+1, n^2+n+1, n^3+n+1 and n^4+n+1 are all semiprime.

Comment: This is to semiprimes A001358 as A219117 is to primes A000040.

I find no solutions 0 < n =< 80.

3^4+3+1 = 85 = 5*17 is semiprime, but 3^3+3+1 = 321 is prime, so 3 is
not in this sequence.

8^4+8+1 = 4105 = 5 * 821 is semiprime, but 8^3+8+1 = 521 is prime, so
8 is not in this sequence.
20^4+20+1 = 160021 = 17 * 9413 is semiprime, and 20^3+20+1 = 8021 = 13
* 617 is semiprime, but 20^2+20+1 = 421 is prime, so 20 is not in this
sequence.
…
80^4 + 80 + 1 = 40960081 = 73 * 561097 is semiprimes, and
80^3 + 80 + 1 = 512081 = 67 * 7643  is semiprime, but
80^2 + 80 + 1 = 6481 is prime.  So 80 is not in the seq.
```