A347212 a(n) is the next Ulam number (A002858) after 2^(n-1).

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

Offset: 0

Author

Frank M Jackson, Sep 02 2021

Keywords

• nonn
• more

Comments

This sequence appears to be a "complete" (sic) sequence as defined in the Wikipedia link.

Examples

			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.
		

Links

• 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]

Crossrefs

Cf. A002858, A331729.

Programs

Mathematica

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}]]

Extensions

a(22)-a(31) from Amiram Eldar, Sep 02 2021