A183233 Ordering of the numbers in the tree A183231; complement of A183234.

1, 3, 4, 6, 7, 10, 11, 13, 15, 16, 18, 19, 21, 22, 24, 25, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 55, 56, 58, 59, 61, 62, 66, 67, 69, 70, 72, 73, 76, 78, 79, 81, 82, 84, 85, 88, 89, 91, 92, 94, 95, 97, 98, 101, 102, 105, 106, 108, 109, 111, 112, 115, 116, 118, 120, 121, 123, 124, 126, 127, 130, 131, 133, 136, 137, 139, 140, 142, 143, 146, 147, 149, 151, 153, 154, 156, 157, 159, 160, 163, 164, 166, 168, 169, 171, 172, 174, 175, 177, 178, 181, 182, 184, 186

Offset

1,2

Links

Table of n, a(n) for n=1..111.

Formula

The monotonic ordering of the numbers in the set S generated by these rules: 1 is in S, and if n is in S, then (n^2+5n+2)/2 and n+Floor(1/2+sqrt(2n+4)) are in S.

Mathematica

  nn=200; t={1}; t0=t; While[t=Select[Union[t, (1/2)*(t^2+5t+2), t+Floor[1/2+(2t+4)^(1/2)]], #<=nn &]; t0 !=t, t0=t]; t
f[s_List] := Select[ Union@ Join[s, (s^2 + 5 s + 2)/2, s + Floor[1/2 + Sqrt@ (2 s + 4)]], # < 201 &]; NestWhile[f, {1}, UnsameQ, All]

Crossrefs

Cf. A183231, A183232, A183234.

Sequence in context: A060832 A341292 A047297 * A191926 A065135 A229792

Adjacent sequences: A183230 A183231 A183232 * A183234 A183235 A183236

Keyword

nonn

Author

Clark Kimberling, Jan 02 2011

Status

approved