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 A376337 #8 Oct 18 2024 18:13:44
%S A376337 3,7,9,31,127,8191,131071,524287
%N A376337 Numbers k such that phi(k)/2 + 1 = phi(k + 1) where phi = A000010.
%C A376337 Conjecture: this sequence is the union {9} and the Mersenne primes A000668.
%e A376337 Number 9 is in this sequence because phi(9)/2 + 1 = 6/2 + 1 = 3 + 1 = 4 is equal to phi(9 + 1) = phi(10) = 4.
%t A376337 Select[Range[550000], EulerPhi[#]/2+1==EulerPhi[#+1] &] (* _Stefano Spezia_, Sep 22 2024 *)
%o A376337 (Magma) [k: k in [3..5*10^6] | ((EulerPhi(k) div 2) + 1) eq EulerPhi(k + 1)];
%Y A376337 Cf. A000010, A000668, A191611, A376338.
%K A376337 nonn,more
%O A376337 1,1
%A A376337 _Juri-Stepan Gerasimov_, Sep 20 2024