A379727 - OEIS

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

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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: A379724 A379725 A379726 * A379728 A379729 A379730

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 31 2024

STATUS

approved