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

1,1

Links

Table of n, a(n) for n=1..39.

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

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 *)

Prog

(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

Crossrefs

Cf. A353889.

Sequence in context: A238506 A308169 A343225 * A276117 A105135 A225552

Adjacent sequences: A363242 A363243 A363244 * A363246 A363247 A363248

Keyword

nonn

Author

Julian Zbigniew Kuryllowicz-Kazmierczak, May 23 2023

Extensions

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

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

Status

approved