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%I #28 Jan 05 2022 11:48:31
%S 1,2,3,6,4,46,5,10,7,22,8,50,9,14,11,18,12,54,13,26,21,30,15,58,16,34,
%T 17,42,19,62,20,38,25,70,31,66,23,74,29,78,24,102982,27,86,41,82,28,
%U 102974,35,98,33,90,32,102978,36,102,37,106,39,102990,40,94,71
%N Companion sequence to A103683: a(n) = k if A103683(k) = n; a(n) = 0 if n is not in {A103683}.
%C A103683 is injective.
%C Inverse of A103683.
%C Conjecture: a(42 + 6*k) = 0. This would follow from the conjecture that for n >= 67, A103683(n) is divisible by 3 iff n == 3 mod 4 and by 2 iff n == 2 mod 4. - _Robert Israel_, May 12 2015
%C The conjecture is false; a(42) = 102982. - _Rémy Sigrist_, Jan 05 2022
%H Rémy Sigrist, <a href="/A105214/b105214.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A105214/a105214_1.txt">C program for A105214</a>
%e a(6) = 46 because A103683(46) = 6.
%t f[s_] := Block[{k = 1, l = Take[s, -3]}, While[ Union[ GCD[k, l]] != {1} || MemberQ[s, k], k++]; Append[s, k]]; Take[Ordering@ Nest[f, {1, 2, 3}, 200], 41] (* _Robert G. Wilson v_, Jun 26 2011 *)
%o (C) See Links section.
%Y Cf. A103683.
%K nonn
%O 1,2
%A _Leroy Quet_ and _Robert G. Wilson v_, Apr 13 2005
%E More terms from _Rémy Sigrist_, Jan 05 2022
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