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 A356450 #14 Aug 16 2023 21:14:47
%S A356450 8,16,17,32,33,34,35,64,65,66,67,68,69,71,128,129,130,131,132,133,134,
%T A356450 135,136,137,139,143,256,257,258,259,260,261,262,263,264,265,266,267,
%U A356450 269,271,272,273,275,279,287,288,384,512,513,514,515,516,517,518,519,520
%N A356450 Positions of numbers m = A005940(n+1) such that m < n.
%C A356450 This sequence contains 2^k for k >= 3. Powers of 2 expressed in binary consist of a 1 followed by k zeros. Therefore, A005940(2^k) = prime(k+1)^1. For k >= 3, 2^k > prime(k+1).
%H A356450 Michael De Vlieger, <a href="/A356450/b356450.txt">Table of n, a(n) for n = 1..13175</a> (terms m < 2^21)
%H A356450 Michael De Vlieger, <a href="/A356450/a356450.png">Fan style binary tree diagram of b(n)</a> for n = 1..2^14-1, where b(n) = A005940(n), highlighting terms such that b(n+1) < n in red, b(n+1) = n in yellow, and b(n+1) > n in blue. Positions of the terms shown in red are in this sequence, while b(A029747(n)+1) = A029747(n) appears in yellow.
%e A356450 34 is in the sequence since A005940(34) = A005940("100010"_2) = prime(1+1)^1 * prime(4+1)^1 = 33, and 33 < 34.
%t A356450 nn = 2^10; a[0] = 1; Reap[Do[k = Prime[1 + DigitCount[n, 2, 0]]*a[n - 2^Floor@ Log2@ n]; Set[a[n], k]; If[k < n, Sow[n]], {n, nn}]][[-1, -1]] (* _Michael De Vlieger_, Aug 07 2022 *)
%Y A356450 Cf. A005940, A029747, A356455.
%K A356450 nonn
%O A356450 1,1
%A A356450 _Michael De Vlieger_, Aug 07 2022