A384191 Unique increasing sequence (a(n)) whose complement, (b(n)), satisfies b(n) = a(a(n))+3.

1, 2, 3, 7, 8, 9, 10, 11, 12, 16, 17, 18, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 40, 41, 42, 46, 47, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 79, 80, 81, 85, 86, 87, 88, 89, 90, 94, 95, 96, 97, 98, 99, 103, 104

Offset

1,2

Comments

For k>=1, the Mathematica program gives solutions of the complementary equation b(n)=a(a(n))+k; if k=1, then a=A000201; if k=2, then a=A137708.

Links

Table of n, a(n) for n=1..65.

Example

a(a(1)) = a(1) = 1, so b(1) = 4.
a(a(2)) = a(2) = 2, so b(2) = 5.
a(a(3)) = a(3) = 3, so b(3) = 6.
a(a(4)) = a(7) = 10, so b(4) = 13.

Mathematica

k = 3; p = k*Array[Floor[#*GoldenRatio] &, 100] ;
seq = ConstantArray[1, Last[p]];
seq[[p]] = k + 1;
u = Join[{1}, Accumulate[seq] + 1]  (* A384191 *)
Complement[Range[Last[#]], #] &[u]  (* A383192 *)
(* Peter J. C. Moses, May 12 2025 *)

Crossrefs

Cf. A000201, A137708, A384192 (complement).

Sequence in context: A244162 A182516 A089008 * A228088 A299497 A047534

Adjacent sequences: A384188 A384189 A384190 * A384192 A384193 A384194

Keyword

nonn

Author

Clark Kimberling, May 21 2025

Status

approved