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

%I A380506 #29 Mar 25 2025 15:03:34
%S A380506 2,3,8,968,17,11068,3070,58836,50835,403831,20143,18829,868283,458530,
%T A380506 245484,46660,199785,5653022,3603103,477958,2144637,187759,910595,
%U A380506 4181867,1692138,7454121,10792662,11232004,36842536,16878596,1339550,211463464,3650538,24922454
%N A380506 Smallest k such that A073734(k) is in A055932, where A073734 is the GCD of consecutive terms of the EKG sequence A064413.
%C A380506 This is a sequence of "late comers" in A073734, that is, numbers with a primorial kernel.
%H A380506 Scott R. Shannon, <a href="/A380506/b380506.txt">Table of n, a(n) for n = 1..46</a>
%e A380506 Let s = A055932.
%e A380506 Table of n, s(n), and a(n) for n = 1..18:
%e A380506  n   s(n)       a(n)
%e A380506 --------------------
%e A380506  1     1          2
%e A380506  2     2          3
%e A380506  3     4          8
%e A380506  4     6        968
%e A380506  5     8         17
%e A380506  6    12      11068
%e A380506  7    16       3070
%e A380506  8    18      58836
%e A380506  9    24      50835
%e A380506 10    30     403831
%e A380506 11    32      20143
%e A380506 12    36      18829
%e A380506 13    48     868283
%e A380506 14    54     458530
%e A380506 15    60     245484
%e A380506 16    64      46660
%e A380506 17    72     199785
%e A380506 18    90    5653022
%t A380506 (* First, load function f from A055932, then generate a064413 using code in the links at that sequence *)
%t A380506 a055932 = Union@ Flatten@ f[4];
%t A380506 a073734 = Table[GCD[a064413[[n]], a064413[[n + 1]]], {n, Length[a064413] - 1}];
%t A380506 TakeWhile[ Map[FirstPosition[a073734, #][[1]] &, a055932], IntegerQ]
%Y A380506 Cf. A002110, A055932, A064413, A073734, A382222 (superset), A382271 (proper subset).
%K A380506 nonn
%O A380506 1,1
%A A380506 _Michael De Vlieger_ and _Scott R. Shannon_, Mar 23 2025