A298297 Numbers k such that b(k+1) = b(k) + 1, where b = A298296.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 81, 83, 84, 86, 87, 88, 90, 92, 94, 95, 97

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Example

b = A298296 = (3,4,5,6,7,8,9,10,11,12,14,15,17,...), so that b(k+1) = b(k) + 1 for k = 1..9 and b(11) = b(10) + 2.

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
a[n_] := a[0]*b[n] + a[1]*b[n - 1]
Table[{a[n], b[n + 1] = mex[Flatten[Map[{a[#], b[#]} &, Range[0, n]]], b[n - 0]]}, {n, 2, 1000}];
u = Table[b[n], {n, 0, 150}]  (* A298296 *)
d = Differences[u]
Flatten[Position[d, 1]]  (* A298297 *)
Flatten[Position[d, 2]]  (* A298298 *)

Crossrefs

Cf. A298296, A297298 (complement).

Sequence in context: A306520 A247945 A317621 * A331009 A225580 A071980

Adjacent sequences: A298294 A298295 A298296 * A298298 A298299 A298300

Keyword

nonn,easy

Author

Clark Kimberling, Apr 12 2018

Status

approved