This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104238 #13 Jun 30 2020 05:43:51 %S A104238 2,10,12,16,22,126,136,180,256,268,276,366,388,396,438,462,606,642, %T A104238 652,658,676,738,760,768,982,1012,1068,1116,1230,1276,1320,1452,1488, %U A104238 1530,1618,1692,1698,1752,1846,1948,1996,2080,2112,2160,2332,2392,2440,2520 %N A104238 Positive integers n such that n^5 + 1 is semiprime. %C A104238 n^5+1 can only be prime when n = 1, n^5+1 = 2. This is because of the polynomial factorization n^5+1 = (n+1) * (n^4 - n^3 + n^2 - n + 1) = (n+1)*A060884(n). Hence after the initial n=1 prime, the binomial can at best be semiprime and that only when both (n+1) and (n^4 - n^3 + n^2 - n + 1) are primes. %H A104238 Robert Price, <a href="/A104238/b104238.txt">Table of n, a(n) for n = 1..1414</a> %F A104238 a(n)^5 + 1 is semiprime. a(n)+1 is prime and a(n)^4 - a(n)^3 + a(n)^2 - a(n) + 1 is prime. %e A104238 n n^5+1 = (n+1) * (n^4 - n^3 + n^2 - n + 1) %e A104238 2 33 = 3 * 11 %e A104238 10 100001 = 11 * 9091 %e A104238 12 248833 = 13 * 19141 %e A104238 16 1048577 = 17 * 61681 %t A104238 Select[Range[2600],PrimeOmega[#^5+1]==2&] (* _Harvey P. Dale_, May 20 2011 *) %t A104238 Select[Range[200000], PrimeQ[# + 1] && PrimeQ[(#^5 + 1)/(# + 1)] &] (* _Robert Price_, Mar 09 2015 *) %Y A104238 Cf. A001358, A103854. %K A104238 easy,nonn %O A104238 1,1 %A A104238 _Jonathan Vos Post_, Apr 02 2005