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 A382119 #27 Apr 07 2025 17:46:15 %S A382119 2,3,4,6,16,126 %N A382119 Numbers k = x*y such that (x*2^k - 1)*(y*2^k - 1) is semiprime. %C A382119 The corresponding semiprimes are 21, 161, 961, 24257, 68718821377, 911862702743865038960621506943417274338971540779454191779448636691549662478337, ... %C A382119 The pairs of primes corresponding to these semiprimes are [1st Mersenne prime, 2nd Mersenne prime], [2nd Mersenne prime, 23], [3rd Mersenne prime, 3rd Mersenne prime], [5th Mersenne prime, 191], [6th Mersenne prime, 7th Mersenne prime], [170141183460469231731687303715884105727, 5359447279004780799548150067050349330431], ... %C A382119 a(7) > 100000. - _Michael S. Branicky_, Mar 31 2025 %e A382119 2 = 1*2, 3 = 1*3, 4 = 2*2, 6 = 2*3, 16 = 2*8, 126 = 2*63. %o A382119 (Magma) [n: n in [1..1000] | not #[d: d in Divisors(n) | IsPrime(d*2^n-1) and IsPrime((n div d)*2^n-1)] eq 0]; %Y A382119 Cf. A000668, A001358, A161904. %K A382119 nonn,more %O A382119 1,1 %A A382119 _Juri-Stepan Gerasimov_, Mar 25 2025