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 A309942 #17 Sep 08 2022 08:46:22 %S A309942 2,10,11,14,21,23,29,39,47,50,53,55,63,71,73,74,75,82,86,95,101,105, %T A309942 113,115,121,142,147,150,167,169,179,181,182,190,199,203,209,233,235, %U A309942 253,277,285,303,307,311,317,335,337,339,342,343,347,349,353,355,358 %N A309942 Numbers k such that 2^k - 1 and 2^k + 1 have the same number of prime factors, counted with multiplicity. %e A309942 a(1) = 2: 2^2 - 1 = 3 and 2^2 + 1 are both prime, %e A309942 a(2) = 10: 2^10 - 1 = 1023 = 3 * 11 * 31 and 2^10 + 1 = 1025 = 5^2 * 41 both have 3 prime factors. %t A309942 Select[Range[200], PrimeOmega[2^# - 1 ] == PrimeOmega[2^# + 1 ] &] (* _Amiram Eldar_, Aug 24 2019 *) %o A309942 (PARI) for(k=1, 209, my(f=bigomega(2^k-1),g=bigomega(2^k+1));if(f==g,print1(k,", "))) %o A309942 (Magma) [m:m in [2..400]| &+[p[2]: p in Factorization(2^m-1)] eq &+[p[2]: p in Factorization(2^m+1)]]; // _Marius A. Burtea_, Aug 24 2019 %Y A309942 Cf. A000051, A000225, A046051, A054992, A067886. %K A309942 nonn %O A309942 1,1 %A A309942 _Hugo Pfoertner_, Aug 24 2019 %E A309942 More terms from _Amiram Eldar_, Aug 24 2019