cp's OEIS Frontend

A284725 a(n) = (1/3) * smallest multiple of 3 missing from [A280864(1), ..., A280864(n-1)].

%I A284725 #24 Nov 26 2017 09:51:16
%S A284725 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 A284725 11,11,11,11,11,11,11,11,11,13,17,17,17,17,17,17,17,17,17,17,17,17,17,
%U A284725 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 A284725 a(n) = (1/3) * smallest multiple of 3 missing from [A280864(1), ..., A280864(n-1)].
%C A284725 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 A284725 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 A284725 Rémy Sigrist, <a href="/A284725/b284725.txt">Table of n, a(n) for n = 1..10000</a>
%H A284725 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 A284725 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 A284725 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 A284725 mex := proc(L)
%p A284725 local k;
%p A284725 for k from 1 do
%p A284725 if not k in L then
%p A284725 return k;
%p A284725 end if;
%p A284725 end do:
%p A284725 end proc:
%p A284725 read b280864;
%p A284725 k:=3; a:=[1,1]; ML:=[]; B:=1;
%p A284725 for n from 2 to 120 do
%p A284725 t:=b280864[n];
%p A284725 if (t mod k) = 0 then
%p A284725 ML:=[op(ML),t/k];
%p A284725 B:=mex(ML);
%p A284725 a:=[op(a),B];
%p A284725 else
%p A284725 a:=[op(a),B];
%p A284725 fi;
%p A284725 od:
%p A284725 a;
%t A284725 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 A284725 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 A284725 Array[a, terms] (* _Jean-François Alcover_, Nov 26 2017, after _Rémy Sigrist_'s program for A280864 *)
%Y A284725 Cf. A280864, A064413, A284724, A280726.
%K A284725 nonn
%O A284725 1,5
%A A284725 _N. J. A. Sloane_, Apr 06 2017