OFFSET
1,2
COMMENTS
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.
This sequence lists rows i such that the last term exceeds that of the previous row.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Plot (x,y) 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).
Michael De Vlieger, Analysis of prime decompositions of terms in this sequence.
EXAMPLE
We list numbers in row i of A217438 below, starting with i, aligned in columns:
1 2 3
2 3
3 4 5
4 5 6 7
5 6 7
6 7
7 8 9 10 11
8 9 10 11
9 10 11
10 11 12 13 14
11 12 13 14 15
12 13 14 15
13 14 15
14 15
1 is in the sequence since it is the first row.
2 is not in the sequence, since the last term (3) in row 2 of A217438 is equal to that of the previous row.
3 is in the sequence since its last term (5) exceeds that of the previous row (3).
Further, we observe the terms in row i breaking through resistance in the previous row at i = {1, 3, 4, 7, 10, 11, ...}
MATHEMATICA
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] ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, May 02 2020
STATUS
approved