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%I #7 Dec 27 2019 16:36:23
%S 9,13,17,21,25,29,33,42,45,49,58,61,65,74,77,81,90,93,97,106,109,113,
%T 122,125,129,138,141,145,149,153,157,161,165,174,177,186,189,193,202,
%U 205,209,213,217,221,225,229,238,241,250,253,257,266,269,273,277,281
%N Solution sequence (a(n)) of the complementary equation a(n) = 5 b(n+1) - b(n), with b(0) = 1.
%C The conditions that (a(n)) and (b(n)) be increasing and complementary force the equation a(n) = 5 b(n+1) - b(n), with initial value b(0) = 1, to have a unique solution; that is, a pair of complementary sequences (a(n)) = (9,13,17,21,25,29,...) and (b(n)) = (1,2,3,4,5,6,7,8,10, ...). Conjecture: {a(n) - 5 n} is unbounded below and above.
%e (See A329387.)
%t mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
%t b = {1}; a = {}; h = 5;
%t Do[AppendTo[b, mex[Flatten[{a, b}], b[[-1]]]];
%t AppendTo[a, h b[[-1]] - b[[-2]]], {250}]; a
%t (* _Peter J. C. Moses_, Sep 07 2019 *)
%Y Cf. A329387, A329389, A329390.
%K nonn
%O 0,1
%A _Clark Kimberling_, Nov 23 2019