cp's OEIS Frontend

A331811 a(n) is the next number after a(n-1) which cannot be represented in the form 2*a(i) and Sum_{j=1..n-1} b_j*a(j) where 0 < i < n, b_j = 1 or 0. The sequence starts: a(1) = 1; a(2) = 2; a(3) = 3; a(4) = 5.

%I A331811 #39 Feb 16 2025 08:33:59
%S A331811 1,2,3,5,12,25,49,73,171,195,512,658,1560,1950,4826,6142,14868,18768,
%T A331811 45920,58204,141660,179196,437264,553672,1349328,1707720,4164392,
%U A331811 5271736,12851568,16267008,39662048,50205520,122401584,154935600,377748224,478159264,1165778688,1475649888
%N A331811 a(n) is the next number after a(n-1) which cannot be represented in the form 2*a(i) and Sum_{j=1..n-1} b_j*a(j) where 0 < i < n, b_j = 1 or 0. The sequence starts: a(1) = 1; a(2) = 2; a(3) = 3; a(4) = 5.
%C A331811 This sequence is a complete sequence.
%H A331811 Rémy Sigrist, <a href="/A331811/a331811.txt">C++ program for A331811</a>
%H A331811 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteSequence.html">Complete Sequence</a>
%t A331811 Nest[Append[#, Block[{k = #[[-1]] + 1}, While[Nand[NoneTrue[#, k == 2 # &], FreeQ[Map[Total, Rest@ Subsets[#]], k]], k++]; k]] & @@ {#, Map[Total, Subsets[#]]} &, {1, 2, 3, 5}, 10] (* _Michael De Vlieger_, Jan 27 2020 *)
%o A331811 (PARI) upto(lim)={my(a=[1, 2, 3, 5], 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 A331811 { upto(200) }
%Y A331811 (C++) See Links section.
%K A331811 nonn
%O A331811 1,2
%A A331811 _Zhandos Mambetaliyev_, Jan 27 2020
%E A331811 a(13)-a(14) from _Hugo Pfoertner_, Jan 27 2020
%E A331811 More terms from _Rémy Sigrist_, Jan 28 2020