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A363245 Lexicographically first sequence of positive integers such that all terms are pairwise coprime and no subset sum is a power of 2.

%I A363245 #34 Jun 14 2023 18:41:49
%S A363245 3,7,10,11,17,31,41,71,169,199,263,337,367,1553,2129,2287,2297,4351,
%T A363245 10433,16391,16433,34829,65543,69557,165887,262151,358481,817153,
%U A363245 952319,1048583,3704737,3932167,4518071,12582919,17305417,17367019,50069497,50593799,87228517
%N A363245 Lexicographically first sequence of positive integers such that all terms are pairwise coprime and no subset sum is a power of 2.
%H A363245 Jon E. Schoenfield, <a href="/A363245/a363245.txt">Magma program</a> (computes first 36 terms).
%t A363245 a = {3}; k = 2; Monitor[Do[While[Or[! Apply[CoprimeQ, Join[a, {k}]], AnyTrue[Map[Log2 @* Total@ Append[#, k] &, Subsets[a]], IntegerQ]], k++]; AppendTo[a, k]; k++, {i, 16}], {i, k}]; a (* _Michael De Vlieger_, Jun 14 2023 *)
%o A363245 (Python)
%o A363245 from math import gcd
%o A363245 from itertools import count, islice
%o A363245 def agen(): # generator of terms
%o A363245     a, ss, pows2, m = [], set(), {1, 2}, 2
%o A363245     for k in count(1):
%o A363245         if k in pows2: continue
%o A363245         elif k > m: m <<= 1; pows2.add(m)
%o A363245         if any(p2-k in ss for p2 in pows2): continue
%o A363245         if any(gcd(ai, k) != 1 for ai in a): continue
%o A363245         a.append(k); yield k
%o A363245         ss |= {k} | {k+si for si in ss if k+si not in ss}
%o A363245         while m < max(ss): m <<= 1; pows2.add(m)
%o A363245 print(list(islice(agen(), 30))) # _Michael S. Branicky_, Jun 09 2023
%Y A363245 Cf. A353889.
%K A363245 nonn
%O A363245 1,1
%A A363245 _Julian Zbigniew Kuryllowicz-Kazmierczak_, May 23 2023
%E A363245 a(23)-a(33) from _Michael S. Branicky_, Jun 07 2023
%E A363245 a(34)-a(39) from _Jon E. Schoenfield_, Jun 09 2023