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 A387197 #22 Sep 02 2025 23:38:38 %S A387197 0,3,4,6,46,59,84,94,124,239,267,366,371,424,616,2139,2299,3523,3563, %T A387197 3843,3923,7627,12751,34798,39911,56568,58779 %N A387197 Numbers k such that 32 * 3^k - 1 is prime. %C A387197 a(28) > 10^5. %C A387197 Conjecture: This sequence intersects with A387201 at k = 4 to form twin primes with center N = 2^5 * 3^4 = 2592 = A027856(10). Any such intersection has to be at an even k because if k is odd, either N-1 or N+1 has to be divisible by 5. A covering system can be constructed that eliminates all other intersections except where k = 4(mod 60), and for k > 4 with k = 4(mod 60), the search up to 10^5 makes the probability of another intersection in this residue class vanishingly small. %H A387197 Ken Clements, <a href="/A387197/a387197_2.py.txt">Python program to calculate covering system.</a> %t A387197 Select[Range[0, 4000], PrimeQ[32 * 3^# - 1] &] (* _Amiram Eldar_, Aug 21 2025 *) %o A387197 (Python) %o A387197 from gmpy2 import is_prime %o A387197 print([ k for k in range(4000) if is_prime(32 * 3**k - 1)]) %Y A387197 Cf. A027856, A003307, A005540, A005541, A385115, A387201. %K A387197 nonn,more,new %O A387197 1,2 %A A387197 _Ken Clements_, Aug 21 2025