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 A369615 #20 Feb 03 2024 10:14:16
%S A369615 4,11,13,23,25,27,47,81,193,383,2187,1594323
%N A369615 Powers of primes (A000961) whose neighbors have a prime number as their greatest odd divisor.
%C A369615 From _Jon E. Schoenfield_, Jan 28 2024: (Start)
%C A369615 If it exists, a(13) > 10^2000.
%C A369615 Conjecture: a(12) = 1594323 is the final term of the sequence.
%C A369615 (End)
%e A369615 (prime = greatest odd divisor of a(n)-1; a(n); prime = greatest odd divisor of a(n)+1): (3; 4; 5), (5; 11; 3), (3; 13; 7), (11; 23; 3), (3; 25; 13), (13; 27; 7), (23; 47; 3), (5; 81; 41), (3; 193; 97), (191; 383; 3), (1093; 2187; 547), (797161; 1594323; 398581).
%t A369615 q[n_] := PrimeQ[n/2^IntegerExponent[n, 2]]; Select[Range[2*10^6], PrimePowerQ[#] && And @@ q /@ {# - 1, # + 1} &] (* _Amiram Eldar_, Jan 28 2024 *)
%o A369615 (Magma) [k: k in [2..1600000] | #Divisors(2*k-2)-#Divisors(k-1) eq 2 and
%o A369615 #PrimeDivisors(k) eq 1 and #Divisors(2*k+2)-#Divisors(k+1) eq 2];
%Y A369615 Intersection of A000961 and A369329.
%Y A369615 Cf. A038550.
%Y A369615 Comparable sequences: A275598, A343973.
%K A369615 nonn,more
%O A369615 1,1
%A A369615 _Juri-Stepan Gerasimov_, Jan 27 2024