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 A375324 #8 Oct 10 2024 16:03:28
%S A375324 245,2189,19685,531443,1594325,129140165,10460353205,31381059611,
%T A375324 847288609445,7625597484989,68630377364885,617673396283949,
%U A375324 1853020188851843,5559060566555525,450283905890997365,36472996377170786405,109418989131512359211,2954312706550833698645
%N A375324 Numbers of the form 3^k + 2 that admit at least one divisor of the form 3^m + 2 with 1 <= m < k.
%C A375324 The sequence is inspired by problem 3, Balkan Mathematical Olympiad 27 April - 2 May 2024, Varna, Bulgaria, (see link).
%C A375324 The sequence is infinite because numbers of the form m = 3^(4*k + 1) + 2 are divisible by 5 = 3^1 + 2.
%H A375324 Balkan Mathematical Olympiad, 2024, <a href="https://bmo2024.org/problems/">Problems</a>
%e A375324 245 = 3^5 + 2 and 245 = 49*5 = 49 * (3^1 + 2), so 245 is a term.
%e A375324 2189 = 3^7 + 2 and 2189 = 11*199 = 199 * (3^2 + 2), so 2189 is a term.
%e A375324 129140165 = 3^17 + 2 and 129140165 = 5*25828033 = (3^1 + 2)*25828033 or 129140165 = 11*11740015 = (3^2 + 2)*11740015, so 129140165 is a term.
%o A375324 (Magma) f:=func<n|PrimeDivisors(n) eq [3]>; [n:n in [3^a+2:a in [1..50]]|exists{d: d in Divisors(n)|d ne n and f(d-2) }];
%Y A375324 Cf. A168607.
%K A375324 nonn
%O A375324 1,1
%A A375324 _Marius A. Burtea_, Sep 15 2024