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 A385564 #23 Jul 09 2025 11:00:52 %S A385564 3,4,5,7,8,19,23,29,32,47,61,97,181,233,307,401,887,1021,1087,1361, %T A385564 1481,2053,2293,5407,5857,11059,14281,27277,27803,36497,44987,53017 %N A385564 Prime powers k such that lcm(1, 2, 3, ..., k)-1 is prime. %C A385564 The prime associated with each a(n) is A057824(n). %C A385564 a(33) > 10^5. Up to 10^5, contains 4, 8, 32 not in subsequence A154524. - _Michael S. Branicky_, Jul 04 2025 %e A385564 k=32 is a prime power, so point at which A003418 attains a new value, namely lcm(1, 2, 3, ..., 32) = 144403552893600, and by subtracting one we get 144403552893599 which is a prime number, so 32 is a member of the sequence. %t A385564 Select[Range[6000],PrimePowerQ[#]&&PrimeQ[Fold[LCM,Range[#]]-1]&] (* _James C. McMahon_, Jul 09 2025 *) %o A385564 (PARI) L=1;for(k=2,6000,!isprimepower(k,&p)&&next();L*=p;ispseudoprime(L-1)&&print1(k,", ")) %Y A385564 Intersection of A057825 and A000961. %Y A385564 Supersequence of A154524. %Y A385564 Cf. A057824, A051453, A003418. %K A385564 nonn %O A385564 1,1 %A A385564 _Jeppe Stig Nielsen_, Jul 03 2025 %E A385564 a(31)-a(32) from _Michael S. Branicky_, Jul 03 2025