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

Robert G. Wilson v rgwv at rgwv.com
Wed Nov 14 03:51:31 CET 2012


Dear Sir,

	Here is the code in Mathematica with its output.

fQ[n_] := Union[ PrimeOmega@# & /@ {n^1 + n + 1, n^2 + n + 1, n^3 + n + 1, n^4 + n + 1}] == {2}; Select[ Range@ 2500, fQ]

{84, 92, 129, 132, 182, 185, 195, 201, 234, 255, 264, 327, 333, 356, 407, 444, 449, 528, 705, 732, 794, 795, 881, 980, 1079, 1095, 1115, 1126, 1241, 1253, 1302, 1431, 1479, 1496, 1574, 1772, 1781, 1799, 1805, 1874, 1922, 2052, 2067, 2316, 2352, 2381, 2420, 2441, 2481}

Sincerely yours, Bob.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of franktaw at netscape.net
Sent: Tuesday, November 13, 2012 6:28 PM
To: seqfan at list.seqfan.eu; seqfan at seqfan.eu
Subject: [seqfan] Re: am asking for help by someone who wants to program in in Mathematica, or MAPLE, or whatever

321 = 3 * 107 is semiprime, so 3 is in the sequence.

Franklin T. Adams-Watters

-----Original Message-----
From: Jonathan Post <jvospost3 at gmail.com>

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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