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%I #43 Jun 11 2023 23:29:15
%S 1,2,3,6,11,18,36,69,131,258,522,1025,2054,4101,8194,16394,32817,
%T 65542,131085,262183,524313,1048588,2097164,4194310,8388624,16777218,
%U 33554433,67108881,134217730,268435473,536870927,1073741861
%N a(n) is the next Ulam number (A002858) after 2^(n-1).
%C This sequence appears to be a "complete" (sic) sequence as defined in the Wikipedia link.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Complete_sequence">"Complete" sequence</a>. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]
%e a(0) = 1 because 1 is the next Ulam number after 2^(-1) = 1/2.
%e a(6) = 36 because 36 is the next Ulam number after 2^5 = 32.
%t ulams={1, 2}; Do[AppendTo[ulams, n=Last[ulams]; While[n++; Length[DeleteCases[Intersection[ulams, n-ulams], n/2, 1, 1]]!= 2]; n], {10^4}]; lst=ulams; nextu[n_] := Module[{m = 1}, While[lst[[m]]<=n, m++]; lst[[m]]]; Join[{1}, Table[nextu[2^(n - 1)], {n, 1, 18}]]
%Y Cf. A002858, A331729.
%K nonn,more
%O 0,2
%A _Frank M Jackson_, Sep 02 2021
%E a(22)-a(31) from _Amiram Eldar_, Sep 02 2021
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