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 A334469 #8 May 05 2020 01:18:23
%S A334469 1,3,4,7,10,11,15,16,22,25,26,31,34,36,41,46,52,56,57,63,64,70,71,76,
%T A334469 79,86,94,96,99,106,116,121,127,131,134,142,146,156,160,162,169,176,
%U A334469 183,190,196,204,214,218,221,222,236,241,246,255,266,274,286,288,296
%N A334469 Indices of zero or positive first differences in A217287.
%C A334469 Starting with i, we increment i to build a chain of consecutive numbers such that all distinct prime factors of ensuing numbers i + 1, i + 2, etc., divide at least one previous number in the chain. We store the chains in an irregular triangle T(i,j) described in A217438.
%C A334469 This sequence lists rows i such that the last term exceeds that of the previous row.
%H A334469 Michael De Vlieger, <a href="/A334469/b334469.txt">Table of n, a(n) for n = 1..10000</a>
%H A334469 Michael De Vlieger, <a href="/A334469/a334469.png">Plot (x,y)</a> of x in rows 1 <= y <= 4096 of A217438 in gray, accentuating rows m (in this sequence) in red where no term x in row (y - 1) exists. (Pixels attributed to A334468 appear in yellow).
%H A334469 Michael De Vlieger, <a href="/A334469/a334469.txt">Analysis of prime decompositions of terms in this sequence.</a>
%e A334469 We list numbers in row i of A217438 below, starting with i, aligned in columns:
%e A334469 1 2 3
%e A334469 2 3
%e A334469 3 4 5
%e A334469 4 5 6 7
%e A334469 5 6 7
%e A334469 6 7
%e A334469 7 8 9 10 11
%e A334469 8 9 10 11
%e A334469 9 10 11
%e A334469 10 11 12 13 14
%e A334469 11 12 13 14 15
%e A334469 12 13 14 15
%e A334469 13 14 15
%e A334469 14 15
%e A334469 1 is in the sequence since it is the first row.
%e A334469 2 is not in the sequence, since the last term (3) in row 2 of A217438 is equal to that of the previous row.
%e A334469 3 is in the sequence since its last term (5) exceeds that of the previous row (3).
%e A334469 Further, we observe the terms in row i breaking through resistance in the previous row at i = {1, 3, 4, 7, 10, 11, ...}
%t A334469 Block[{nn = 2^9, r}, r = Array[If[# == 1, 0, Total[2^(PrimePi /@ FactorInteger[#][[All, 1]] - 1)]] &, nn]; Position[Prepend[#, 1], _?(# > 0 &)][[All, 1]] &@ Differences@ Array[Block[{k = # + 1, s = r[[#]]}, While[UnsameQ[s, Set[s, BitOr[s, r[[k]] ] ] ], k++]; k] &, nn - Ceiling@ Sqrt@ nn] ]
%Y A334469 Cf. A217287, A217438, A334468.
%K A334469 nonn
%O A334469 1,2
%A A334469 _Michael De Vlieger_, May 02 2020