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%I #8 May 11 2019 02:23:01
%S 1,2,3,4,6,7,9,10,12,13,14,15,17,18,19,21,22,23,24,26,27,28,30,31,32,
%T 33,35,36,37,39,40,42,43,45,46,47,48,50,51,52,54,55,57,58,59,60,62,63,
%U 64,66,67,69,70,72,73,74,75,77,78,79,81,82,84,85,86,87
%N a(n) is the least number not 2a(m) + a(m-1) for any m < n.
%C Conjectures: Let d(n) = 3a(n) - 4n; then d(n) is bounded, and d(n) = 0 for infinitely many n.
%H Clark Kimberling, <a href="/A325597/b325597.txt">Table of n, a(n) for n = 1..10000</a>
%e Necessarily, a(1) = 1 and a(2) = 2. Because of these values, 5 is the least number not in the sequence, so that a(3) = 3 and a(4) = 4. Consequently, 8 and 11 are disallowed, so a(5) = 6 and a(6) = 7.
%t mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a (* A325597 *)
%t c = Complement[Range[Last[a]], a] (* A325598 *)
%t da = Differences[a] (* A325599 *)
%t Flatten[Position[da, 1]] (* A325600 *)
%t Flatten[Position[da, 2]] (* A325601 *)
%t (* _Peter J. C. Moses_, May 07 2019 *)
%Y Cf. A325598, A325599, A325417.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, May 10 2019
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