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 A137709 #20 May 30 2025 23:53:07
%S A137709 3,4,9,10,13,14,19,20,25,26,29,30,35,36,39,40,45,46,51,52,55,56,61,62,
%T A137709 67,68,71,72,77,78,81,82,87,88,93,94,97,98,103,104,107,108,113,114,
%U A137709 119,120,123,124,129,130,135,136,139,140,145,146,149,150,155,156
%N A137709 Secondary upper Wythoff sequence.
%C A137709 This sequence is the ordered union of even numbered columns of the Wythoff secondary array, A137707. See A137707 for complementary equations of which this sequence is a solution.
%F A137709 a(2n) = 2*A001950(n) = a(2n-1)+1; A001950 is the upper Wythoff sequence.
%e A137709 The upper Wythoff sequence begins with 2,5,7,10,13,15,18,...
%e A137709 Double these: 4,10,14,20,26,30,36,...; subtract 1: 3,9,13,19,25,29,35,...;
%e A137709 Then merge: 3,4,9,10,13,14,19,20,25,26,29,30,35,36,...
%t A137709 Union[Flatten[{#, # - 1}]] &[2 Array[Floor[#*GoldenRatio^2] &, 20]] (* _Peter J. C. Moses_, May 12 2025 *)
%o A137709 (Python)
%o A137709 from math import isqrt
%o A137709 def A137709(n): return (((m:=n+1>>1)+isqrt(5*m**2)>>1)+m<<1)-(n&1) # _Chai Wah Wu_, May 30 2025
%Y A137709 Cf. A001950, A035513, A137707, A137708.
%K A137709 nonn,easy
%O A137709 1,1
%A A137709 _Clark Kimberling_, Feb 07 2008