OFFSET
1,2
COMMENTS
Most of the pairs are of the form (r,2r+1) except for the ones like a(4) = (8,18) and a(12) = (28,58) and (38,78) etc. which are of the form (r,2r +2).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
Let A(n) = A007814(n). Let B(n) = A(n) + 1 if A(n) < 2; B(n) = 0 if A(n)>=2 & A(n) is even; B(n) = 2 if A(n) >= 2 & A(n) is odd. Then a(n) = (5n+B(n)-4)/2. - John Chew (jjchew(AT)math.utoronto.ca), Jun 20 2006
EXAMPLE
The first pair (1, 3) covers 1, 2, 3. The second pair is (4, 9) covering 4, 5, 9.
MATHEMATICA
(* Here, the offset for (a(n)) is 0. *)
z = 200;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a = {}; b = {}; c = {};
Do[AppendTo[a,
mex[Flatten[{a, b, c}], If[Length[a] == 0, 1, Last[a]]]];
AppendTo[b, mex[Flatten[{a, b, c}], Last[a]]];
AppendTo[c, Last[a] + Last[b]], {z}];
Take[a, 100] (* A075325 *)
Take[b, 100] (* A047215 *)
Take[c, 100] (* A075326 *)
Grid[{Join[{"n"}, Range[0, 20]], Join[{"a(n)"}, Take[a, 21]],
Join[{"b(n)"}, Take[b, 21]], Join[{"c(n)"}, Take[c, 21]]},
Alignment -> ".",
Dividers -> {{2 -> Red, -1 -> Blue}, {2 -> Red, -1 -> Blue}}]
(* Peter J. C. Moses, Apr 26 2018 *)
PROG
(PARI) used = vector(500); i = 1; A = vector(80); B = A; C = A; for (n = 1, 80, while (used[i], i++); j = i + 1; while (used[j] || used [i + j], j++); A[n] = i; B[n] = i + j; C[n] = i + i + j; used[i] = 1; used[j] = 1; used[i + j] = 1); A \\ David Wasserman, Jan 16 2005
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 16 2002
EXTENSIONS
More terms from David Wasserman, Jan 16 2005
STATUS
approved