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A284724
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a(n) = (1/2) * smallest even number missing from [A280864(1), ..., A280864(n-1)].
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4
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1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 10, 12, 13, 13, 13, 15, 15, 15, 15, 16, 16, 16, 16, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 22, 22, 22, 22, 22, 25, 25, 25, 25, 25, 27, 27, 27, 28, 28, 28, 30, 30, 30, 30, 32, 32, 32, 32, 33, 33, 33, 35, 35, 35, 35, 36, 36, 36, 36, 40, 40, 40, 42
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OFFSET
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1,3
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COMMENTS
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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_2(n)/2.
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.
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LINKS
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J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002.
J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG Sequence, Exper. Math. 11 (2002), 437-446.
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EXAMPLE
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The initial terms of A280864 are 1,2,4,3,6,8,... The smallest missing even number from [1,2,4,3,6] is 8, so a(6) = 8/2 = 4.
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MAPLE
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mex := proc(L)
local k;
for k from 1 do
if not k in L then
return k;
end if;
end do:
end proc:
read b280864;
k:=2; a:=[1, 1]; ML:=[]; B:=1;
for n from 2 to 120 do
t:=b280864[n];
if (t mod k) = 0 then
ML:=[op(ML), t/k];
B:=mex(ML);
a:=[op(a), B];
else
a:=[op(a), B];
fi;
od:
a;
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MATHEMATICA
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terms = 80; 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]];
Clear[a];
a[1] = 1;
a[n_] := a[n] = For[b = 2a[n-1], True, b += 2, If[FreeQ[A280864[[1 ;; n-1]], b], Return[b/2]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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