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 A344185 #20 May 13 2021 06:04:18
%S A344185 0,3,3,3,5,3,3,27,3,9,5,9,27,33,3,43,9,9,39,9,5,3,33,27,9,27,39,3,5,3,
%T A344185 9,141,75,27,5,53,63,99,17,57,9,39,89,33,27,3,33,45,113,29,75,9,71,
%U A344185 125,71,149,17,99,123,3,39,105,3,27,27,9,39,163,101,43
%N A344185 a(n) = A344141(n) - 2^n.
%C A344185 A more intuitive version of A344141.
%C A344185 Every term other than the first is a member of A129771.
%C A344185 In A057496 it is stated that if x^n + x^3 + x^2 + x + 1 is irreducible, then so is x^n + x^3 + 1. It follows that no term can be equal to 15.
%C A344185 It is conjectured that no term can be of the form P_m(2^k), where P_m(x) = Product_{i>=0} (1 + x^(2^(d_i)))^(c_i) if the binary representation of m is m = Sum_{i>=0} c_i * 2^(d_i), k is an odd number. See my conjecture in A344177.
%H A344185 Jianing Song, <a href="/A344185/b344185.txt">Table of n, a(n) for n = 1..1000</a>
%e A344185 See A344141.
%o A344185 (PARI) A344185(n) = for(k=0, 2^n-1, if(polisirreducible(Mod(Pol(binary(2^n+k)), 2)), return(k)))
%Y A344185 Cf. A014580, A344141, A344186, A129771, A344177.
%K A344185 nonn
%O A344185 1,2
%A A344185 _Jianing Song_, May 11 2021