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

1,4

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.

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.

Example

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.

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 *)

Crossrefs

Cf. A280864, A064413, A284724, A280725.

Sequence in context: A026819 A302342 A137214 * A319951 A222642 A081832

Adjacent sequences: A284723 A284724 A284725 * A284727 A284728 A284729

Keyword

nonn

Author

N. J. A. Sloane, Apr 06 2017

Status

approved