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 A186771 #21 Apr 16 2025 05:29:13
%S A186771 1,2,3,6,12,27,48,130,252,705,1386,2295,7125,17316,31959,51054,74601,
%T A186771 102600,351315,748440,2123189,4198848,6975417,10452896,14631285,
%U A186771 19510584,25090793,31371912,38353941,46036880,54420729,63505488,73291157,83777736,94965225,106853624,119442933,132733152
%N A186771 Numbers m such that A186711(m) = 1.
%C A186771 Greatest common divisor of A003586(a(n)) and A003586(a(n)+1) is 1.
%F A186771 A186927(n) = A003586(a(n)); A186928(n) = A003586(a(n) + 1).
%e A186771 n = 12, a(12) = 2295:
%e A186771 A003586(2295) = 19342813113834066795298816 = 2^84,
%e A186771 A003586(2296) = 19383245667680019896796723 = 3^53 and GCD(2^84,3^53) = 1.
%t A186771 seq[lim_] := Module[{s = {}, pow3, c2, c3a, c3b}, Do[c2 = c[2^i]; pow3 = 3^Floor[i*Log[3, 2]]; c3a = c[pow3]; c3b = c[3*pow3]; If[c3a + 1 == c2, AppendTo[s, c3a]]; If[c2 + 1 == c3b, AppendTo[s, c2]], {i, 0, c[lim]}]; s]; c[n_] := Sum[1 + Floor[Log[3, n/2^i]], {i, 0, Log2[n]}]; seq[10^14] (* _Amiram Eldar_, Apr 16 2025 *)
%o A186771 (Haskell)
%o A186771 import Data.List (findIndices)
%o A186771 a186771 n = a186771_list !! (n-1)
%o A186771 a186771_list = map (+ 1) $ findIndices (== 1) a186711_list
%o A186771 (PARI) c(n) = sum(i=0, logint(n, 2), 1 + logint(n\2^i, 3));
%o A186771 list(lim) = {my(pow3, c2, c3a, c3b); for(i = 0, c(lim), c2 = c(2^i); pow3 = 3^logint(2^i, 3); c3a = c(pow3); c3b = c(3*pow3); if(c3a + 1 == c2, print1(c3a, ", ")); if(c2 + 1 == c3b, print1(c2, ", ")));} \\ _Amiram Eldar_, Apr 16 2025
%Y A186771 Cf. A003586, A186711, A186927, A186928.
%K A186771 nonn
%O A186771 1,2
%A A186771 _Reinhard Zumkeller_, Feb 26 2011
%E A186771 a(22)-a(33) from _Donovan Johnson_, Mar 04 2011
%E A186771 a(34)-a(38) from _Amiram Eldar_, Apr 16 2025