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%I #24 Nov 26 2017 09:51:16
%S 1,1,1,1,2,3,3,3,3,3,5,5,5,5,5,5,5,7,7,7,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T 11,11,11,11,11,11,11,11,11,13,17,17,17,17,17,17,17,17,17,17,17,17,17,
%U 17,17,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,23,23,23,27,27,27,27,27,27,27,27
%N a(n) = (1/3) * smallest multiple of 3 missing from [A280864(1), ..., A280864(n-1)].
%C For k >= 1, n >= 1, let B_k(n) = smallest multiple of k missing from [A280864(1), ..., A280864(n-1)]. Sequence gives values of B_3(n)/3.
%C The analogous sequences B_k(n) for the EKG sequence A064413 were important for the analysis of that sequence, so they may also be useful for studying A280864.
%H Rémy Sigrist, <a href="/A284725/b284725.txt">Table of n, a(n) for n = 1..10000</a>
%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0204011">The EKG sequence</a>, arXiv:math/0204011 [math.NT], 2002.
%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.3/Lagarias437_446.pdf">The EKG Sequence</a>, Exper. Math. 11 (2002), 437-446.
%e The initial terms of A280864 are 1,2,4,3,6,8,... The smallest missing multiple of 3 in [1,2,4,3,6] is 9, so a(6) = 9/3 = 3.
%p mex := proc(L)
%p local k;
%p for k from 1 do
%p if not k in L then
%p return k;
%p end if;
%p end do:
%p end proc:
%p read b280864;
%p k:=3; a:=[1,1]; ML:=[]; B:=1;
%p for n from 2 to 120 do
%p t:=b280864[n];
%p if (t mod k) = 0 then
%p ML:=[op(ML),t/k];
%p B:=mex(ML);
%p a:=[op(a),B];
%p else
%p a:=[op(a),B];
%p fi;
%p od:
%p a;
%t terms = 85; rad[n_] := Times @@ FactorInteger[n][[All, 1]]; A280864 = Reap[present = 0; p = 1; pp = 1; Do[forbidden = GCD[p, pp]; mandatory = p/forbidden; a = mandatory; While[BitGet[present, a] > 0 || GCD[forbidden, a] > 1, a += mandatory]; Sow[a]; present += 2^a; pp = p; p = rad[a], terms]][[2, 1]];
%t Clear[a]; a[1] = 1; a[n_] := a[n] = For[b = 3 a[n - 1], True, b += 3, If[FreeQ[A280864[[1 ;; n - 1]], b], Return[b/3]]];
%t Array[a, terms] (* _Jean-François Alcover_, Nov 26 2017, after _Rémy Sigrist_'s program for A280864 *)
%Y Cf. A280864, A064413, A284724, A280726.
%K nonn
%O 1,5
%A _N. J. A. Sloane_, Apr 06 2017
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