[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
about 80 seconds. They start
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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