A379727 a(1) = 1. For n > 1, a(n) = smallest prime factor of c=2*a(n-1)+1 that is not in {a(1), ..., a(n-1)}; if all prime factors of c are in {a(1), ..., a(n-1)}, then we try the next value of c, which is 2*c+1; and so on.

1, 3, 7, 5, 11, 23, 47, 19, 13, 37, 151, 101, 29, 59, 17, 71, 41, 83, 167, 67, 271, 181, 727, 97, 1567, 6271, 113, 227, 911, 1823, 521, 149, 599, 109, 73, 197, 79, 53, 107, 43, 563, 347, 139, 31, 127, 89, 179, 359, 719, 1439, 2879, 443, 887, 7103, 14207, 5683, 421, 281, 1289, 2579, 607, 1621, 499, 1999, 5333, 10667, 251, 503, 733, 163, 131, 263, 211, 3391, 13567, 7753, 1723, 383, 307, 1231, 821, 173, 293

Offset

1,2

Comments

If we start with a(1) = 2, we get A379652.

Links

Robert C. Lyons, Table of n, a(n) for n = 1..10000

Mathematica

c[_] := True; j = 1; c[1] = False;
{j}~Join~Reap[Do[
  m = 2*j + 1;
  While[
    Set[k, SelectFirst[FactorInteger[m][[All, 1]], c]]; !
      IntegerQ[k], m = 2*m + 1]; c[k] = False;
j = Sow[k], {120}] ][[-1, 1]] (* Michael De Vlieger, Dec 31 2024 *)

Prog

(Python)
from sympy import primefactors
seq = [1]
seq_set = set(seq)
max_seq_len=100
while len(seq) <= max_seq_len:
    c = seq[-1]
    done = False
    while not done:
        c = 2*c+1
        factors = primefactors(c)
        for factor in factors:
            if factor not in seq_set:
                seq.append(factor)
                seq_set.add(factor)
                done = True
                break
print(seq) # Robert C. Lyons, Jan 01 2025

Crossrefs

Cf. A379652, A379649.

Sequence in context: A074368 A074588 A287865 * A238086 A065175 A065283

Adjacent sequences: A379721 A379723 A379726 * A379728 A379729 A379732

Keyword

nonn,new

Author

N. J. A. Sloane, Dec 31 2024

Status

approved