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 A147613 #29 Apr 18 2025 17:44:33
%S A147613 2,4,6,7,8,9,10,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,
%T A147613 31,32,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,
%U A147613 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77
%N A147613 Numbers that are not Jacobsthal numbers.
%C A147613 The nonnegative integers not occurring in A001045.
%C A147613 A147612(a(n)) = 0.
%C A147613 The formula below is a consequence of the Lambek-Moser theorem.
%H A147613 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambek%E2%80%93Moser_theorem">Lambek-Moser theorem</a>
%F A147613 a(n) = floor(-LambertW(-1, -(1/3)*log(2)*2^(3/2-n))/log(2) + 1/2). - Nicolas Normand (Nicolas.Normand(at)polytech.univ-nantes.fr), Nov 29 2017
%F A147613 a(n) = m+1 if m>=A001045(floor(log_2(3*n+1))+1) and a(n) = m otherwise, where m = n-1+floor(log_2(3*n+1)). - _Chai Wah Wu_, Apr 17 2025
%p A147613 a:=proc(n) floor(-LambertW(-1,-1/3*ln(2)*2^(3/2-n))/ln(2)+1/2) end:
%p A147613 seq(a(n), n=1..70); # _Simon Plouffe_, Nov 29 2017
%t A147613 Complement[Range[m = 100], LinearRecurrence[{1, 2}, {0, 1}, m]] (* _Jean-François Alcover_, Feb 13 2018 *)
%o A147613 (Python)
%o A147613 def A147613(n): return (m:=n-2+(k:=(3*n+1).bit_length()))+(m>=((1<<k)|1)//3) # _Chai Wah Wu_, Apr 17 2025
%Y A147613 Cf. A001045.
%K A147613 nonn
%O A147613 1,1
%A A147613 _Reinhard Zumkeller_, Nov 08 2008