A298298 Numbers k such that b(k+1) = b(k) + 2, where b = A298296.

10, 12, 14, 16, 18, 20, 22, 24, 27, 31, 34, 38, 41, 45, 48, 52, 55, 59, 62, 66, 69, 73, 76, 80, 82, 85, 89, 91, 93, 96, 100, 102, 105, 109, 111, 113, 116, 120, 122, 125, 129, 131, 133, 136, 140, 142, 145, 149

Offset: 1

Author

Clark Kimberling, Apr 12 2018

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A298296, A297297 (complement).

Programs

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 *)