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%I #8 Apr 21 2021 03:50:20
%S 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,
%T 39,40,42,43,44,46,47,49,50,51,53,54,56,57,58,60,61,63,64,65,67,68,70,
%U 71,72,74,75,77,78,79,81,83,84,86,87,88,90,92,94,95,97
%N Numbers k such that b(k+1) = b(k) + 1, where b = A298296.
%e 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.
%t mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
%t a[n_] := a[0]*b[n] + a[1]*b[n - 1]
%t Table[{a[n], b[n + 1] = mex[Flatten[Map[{a[#], b[#]} &, Range[0, n]]], b[n - 0]]}, {n, 2, 1000}];
%t u = Table[b[n], {n, 0, 150}] (* A298296 *)
%t d = Differences[u]
%t Flatten[Position[d, 1]] (* A298297 *)
%t Flatten[Position[d, 2]] (* A298298 *)
%Y Cf. A298296, A297298 (complement).
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Apr 12 2018
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