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A331800 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.

%I A331800 #51 Feb 16 2025 08:33:59
%S A331800 1,3,5,7,17,19,50,64,152,190,470,598,1448,1828,4472,5668,13796,17452,
%T A331800 42584,53920,131408,166312,405560,513400,1251584,1584208,3862592,
%U A331800 4889392,11920400,15088816,36788000,46566784,113532416,143710048,350376032,443509600,1081305728
%N A331800 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 A331800 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 A331800 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BrownsCriterion.html">Brown's Criterion</a>
%H A331800 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteSequence.html">Complete Sequence</a>
%o A331800 (PARI) /* a(n) for n>0 */
%o A331800 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 A331800 { upto(200) }
%Y A331800 Cf. A331809, A331811.
%K A331800 nonn
%O A331800 1,2
%A A331800 _Zhandos Mambetaliyev_, Jan 26 2020
%E A331800 a(13)-a(14) from _Hugo Pfoertner_, Jan 27 2020
%E A331800 More terms, using _Rémy Sigrist_'s C++ at A331811 from _Hugo Pfoertner_, Jan 28 2020