%I #50 Feb 29 2020 11:27:28

%S 1,3,5,7,17,19,50,64,152,190,470,598,1448,1828,4472,5668,13796,17452,

%T 42584,53920,131408,166312,405560,513400,1251584,1584208,3862592,

%U 4889392,11920400,15088816,36788000,46566784,113532416,143710048,350376032,443509600,1081305728

%N a(1) = 1; thereafter a(n) is the smallest number > a(n-1) which is neither of the form 2*a(i) nor Sum_{j=1..n-1} ( b_j*a(j) ) where 0 < i < n, b_j = 0 or 1.

%C Inserting the additional term a(0) = 2 would result in a so-called complete sequence after sorting. (The sorted sequence will then meet Brown's criterion.)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BrownsCriterion.html">Brown's Criterion</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteSequence.html">Complete Sequence</a>

%o (PARI) /* a(n) for n>0 */

%o upto(lim)={my(a=[1], b=[]); for(i=1, lim, forsubset(#a, x, b=concat(b, [vecsum(vecextract(a, x))])); b=setminus(vecsort(b, , 8), a); for(j=1, #a, b=concat(b, [2*a[j]]); b=vecsort(b, , 8)); if(setsearch(b, i)==0, a=concat(a, [i]); a=vecsort(a, , 8)) ); a}

%o { upto(200) }

%Y Cf. A331809, A331811.

%K nonn

%O 1,2

%A _Zhandos Mambetaliyev_, Jan 26 2020

%E a(13)-a(14) from _Hugo Pfoertner_, Jan 27 2020

%E More terms, using _Rémy Sigrist_'s C++ at A331811 from _Hugo Pfoertner_, Jan 28 2020