A380506 Smallest k such that A073734(k) is in A055932, where A073734 is the GCD of consecutive terms of the EKG sequence A064413.

2, 3, 8, 968, 17, 11068, 3070, 58836, 50835, 403831, 20143, 18829, 868283, 458530, 245484, 46660, 199785, 5653022, 3603103, 477958, 2144637, 187759, 910595, 4181867, 1692138, 7454121, 10792662, 11232004, 36842536, 16878596, 1339550, 211463464, 3650538, 24922454

Offset: 1

Author

Michael De Vlieger and Scott R. Shannon, Mar 23 2025

Keywords

• nonn

Comments

This is a sequence of "late comers" in A073734, that is, numbers with a primorial kernel.

Examples

			Let s = A055932.
Table of n, s(n), and a(n) for n = 1..18:
 n   s(n)       a(n)
--------------------
 1     1          2
 2     2          3
 3     4          8
 4     6        968
 5     8         17
 6    12      11068
 7    16       3070
 8    18      58836
 9    24      50835
10    30     403831
11    32      20143
12    36      18829
13    48     868283
14    54     458530
15    60     245484
16    64      46660
17    72     199785
18    90    5653022
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A002110, A055932, A064413, A073734, A382222 (superset), A382271 (proper subset).

Programs

Mathematica

(* First, load function f from A055932, then generate a064413 using code in the links at that sequence *)
a055932 = Union@ Flatten@ f[4];
a073734 = Table[GCD[a064413[[n]], a064413[[n + 1]]], {n, Length[a064413] - 1}];
TakeWhile[ Map[FirstPosition[a073734, #][[1]] &, a055932], IntegerQ]