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 A249903 #28 Sep 08 2022 08:46:10
%S A249903 1,2,9,729
%N A249903 Numbers n such that 2n+1 and sigma(n) are both noncomposite numbers.
%C A249903 If a(5) exists, it must be a square bigger than 3*10^8.
%C A249903 Intersection of A005097 and A023194.
%C A249903 Conjecture: 2 and 9 are the only numbers n such that 2n - 1, 2n + 1 and sigma(n) are all primes.
%C A249903 From _Hiroaki Yamanouchi_, Nov 19 2014: (Start)
%C A249903 a(n) (n >= 3) must be of the form 3^(2k) for some positive integer k.
%C A249903 a(5) (if it exists) >= 3^877000 (see A003306 and A028491).
%C A249903 (End)
%e A249903 Number 729 is in the sequence because 2*729 + 1 = 1459 and sigma(729) = 1093 (both primes).
%t A249903 Join[{1}, Select[Range[0, 1000], PrimeQ[DivisorSigma[1, #]]&& PrimeQ[2 # + 1] &]] (* _Vincenzo Librandi_, Nov 14 2014 *)
%t A249903 Join[{1},Select[Range[1000],AllTrue[{2#+1,DivisorSigma[1,#]},PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 06 2019 *)
%o A249903 (Magma) [1] cat [n: n in [1..10000000] | IsPrime(2*n+1) and IsPrime(SumOfDivisors(n))]; // corrected by _Vincenzo Librandi_, Nov 14 2014
%Y A249903 Cf. A000203, A003306, A005097, A023194, A028491, A249902.
%K A249903 nonn,more
%O A249903 1,2
%A A249903 _Jaroslav Krizek_, Nov 14 2014