A334469 Indices of zero or positive first differences in A217287.

1, 3, 4, 7, 10, 11, 15, 16, 22, 25, 26, 31, 34, 36, 41, 46, 52, 56, 57, 63, 64, 70, 71, 76, 79, 86, 94, 96, 99, 106, 116, 121, 127, 131, 134, 142, 146, 156, 160, 162, 169, 176, 183, 190, 196, 204, 214, 218, 221, 222, 236, 241, 246, 255, 266, 274, 286, 288, 296

Offset: 1

Author

Michael De Vlieger, May 02 2020

Keywords

• nonn

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.

Examples

			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, ...}
		

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.

Crossrefs

Cf. A217287, A217438, A334468.

Programs

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] ]