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A347212
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a(n) is the next Ulam number (A002858) after 2^(n-1).
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0
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1, 2, 3, 6, 11, 18, 36, 69, 131, 258, 522, 1025, 2054, 4101, 8194, 16394, 32817, 65542, 131085, 262183, 524313, 1048588, 2097164, 4194310, 8388624, 16777218, 33554433, 67108881, 134217730, 268435473, 536870927, 1073741861
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OFFSET
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0,2
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COMMENTS
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This sequence appears to be a "complete" (sic) sequence as defined in the Wikipedia link.
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LINKS
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Wikipedia, "Complete" sequence. [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]
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EXAMPLE
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a(0) = 1 because 1 is the next Ulam number after 2^(-1) = 1/2.
a(6) = 36 because 36 is the next Ulam number after 2^5 = 32.
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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