A284726 a(n) = (1/4) * smallest multiple of 4 missing from [A280864(1), ..., A280864(n-1)].

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 21, 21, 21, 22, 22

Offset: 1

Author

N. J. A. Sloane, Apr 06 2017

Keywords

• nonn

Comments

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_4(n)/4.

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.

Examples

			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 8, so a(6) = 8/4 = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A280864, A064413, A284724, A280725.

Programs

Maple

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:=4; 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;

Mathematica

terms = 84; 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 = 4 a[n - 1], True, b += 4, If[FreeQ[A280864[[1 ;; n - 1]], b], Return[b/4]]];
Array[a, terms] (* Jean-François Alcover, Nov 26 2017, after Rémy Sigrist's program for A280864 *)