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

Charles Greathouse charles.greathouse at case.edu
Wed Nov 14 00:26:42 CET 2012

```Using my script in A046315 as a starting point, together with an
early-abort semiprime detection program, I found the first 10,000 terms in
84, 92, 129, 132, 182, 185, 195, 201, 234, 255, ...
so you were close to finding the first.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Nov 13, 2012 at 5:45 PM, Jonathan Post <jvospost3 at gmail.com> wrote:

> 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.
>
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```