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 A356455 #9 Aug 09 2022 02:04:45
%S A356455 7,11,14,13,22,33,28,17,26,39,44,65,66,56,19,34,51,52,85,78,117,88,
%T A356455 119,130,132,112,23,38,57,68,95,102,153,104,133,170,255,156,234,176,
%U A356455 209,238,260,264,224,247,361,29,46,69,76,115,114,171,136,161,190,285,204
%N A356455 Numbers m = A005940(n) such that A005940(n) < (n-1), listed in order of appearance in A005940.
%C A356455 Primes p > 5 are in the sequence. We may rewrite the k-th prime p instead as prime(k)^1, and thus convert it to a single run of 1 ones followed by (k-1) zeros, which becomes a binary number consisting of 1 followed by k-1 zeros. It is clear that for p > 5, prime(k) < 2^(k-1).
%H A356455 Michael De Vlieger, <a href="/A356455/b356455.txt">Table of n, a(n) for n = 1..13175</a> (terms in A005940 for n < 2^21)
%H A356455 Michael De Vlieger, <a href="/A356455/a356455.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 ochre, and b(n+1) > n in blue. Terms shown in red appear in this sequence, while b(A029747(n)+1) = A029747(n) appears in ochre.
%e A356455 7 is in the sequence since 7 = prime(3+1)^1, which we write as 1 following 3 zeros when approached from the least significant digit, i.e., "1000"_2 = 8, thus A005940(8) = 7; and 7 < 8.
%e A356455 5 is not in the sequence since 5 = prime(2+1)^1 -> "100"_2 = 4, and 5 > 4.
%e A356455 14 is in the sequence since 14 = prime(0+1)^1 * prime(3+1)^1, which we can express as a binary number with singleton 1s following 0 and 3 zeros, i.e., "10001"_2 = 17, hence A005940(17) = 14 and we see 14 < 17.
%e A356455 33 is in the sequence since 33 = prime(1+1)^1 * prime(4+1)^1 = A005940("100010"_2) = A005940(34) = 33, and we see 33 < 34.
%t A356455 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[k]], {n, nn}]][[-1, -1]]
%Y A356455 Cf. A005940, A029747, A356450.
%K A356455 nonn
%O A356455 1,1
%A A356455 _Michael De Vlieger_, Aug 07 2022