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

3, 7, 10, 11, 17, 31, 41, 71, 169, 199, 263, 337, 367, 1553, 2129, 2287, 2297, 4351, 10433, 16391, 16433, 34829, 65543, 69557, 165887, 262151, 358481, 817153, 952319, 1048583, 3704737, 3932167, 4518071, 12582919, 17305417, 17367019, 50069497, 50593799, 87228517

Offset: 1

Author

Julian Zbigniew Kuryllowicz-Kazmierczak, May 23 2023

Keywords

• nonn

Links

• Jon E. Schoenfield, Magma program (computes first 36 terms).

Crossrefs

Cf. A353889.

Programs

Mathematica

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 *)

Python

from math import gcd
from itertools import count, islice
def agen(): # generator of terms
    a, ss, pows2, m = [], set(), {1, 2}, 2
    for k in count(1):
        if k in pows2: continue
        elif k > m: m <<= 1; pows2.add(m)
        if any(p2-k in ss for p2 in pows2): continue
        if any(gcd(ai, k) != 1 for ai in a): continue
        a.append(k); yield k
        ss |= {k} | {k+si for si in ss if k+si not in ss}
        while m < max(ss): m <<= 1; pows2.add(m)
print(list(islice(agen(), 30))) # Michael S. Branicky, Jun 09 2023

Extensions

a(23)-a(33) from Michael S. Branicky, Jun 07 2023

a(34)-a(39) from Jon E. Schoenfield, Jun 09 2023