A379727 - OEIS

%I #20 Jan 02 2025 09:34:56

%S 1,3,7,5,11,23,47,19,13,37,151,101,29,59,17,71,41,83,167,67,271,181,

%T 727,97,1567,6271,113,227,911,1823,521,149,599,109,73,197,79,53,107,

%U 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

%N 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.

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

%H Robert C. Lyons, <a href="/A379727/b379727.txt">Table of n, a(n) for n = 1..10000</a>

%t c[_] := True; j = 1; c[1] = False;

%t {j}~Join~Reap[Do[

%t   m = 2*j + 1;

%t   While[

%t     Set[k, SelectFirst[FactorInteger[m][[All, 1]], c]]; !

%t       IntegerQ[k], m = 2*m + 1]; c[k] = False;

%t j = Sow[k], {120}] ][[-1, 1]] (* _Michael De Vlieger_, Dec 31 2024 *)

%o (Python)

%o from sympy import primefactors

%o seq = [1]

%o seq_set = set(seq)

%o max_seq_len=100

%o while len(seq) <= max_seq_len:

%o     c = seq[-1]

%o     done = False

%o     while not done:

%o         c = 2*c+1

%o         factors = primefactors(c)

%o         for factor in factors:

%o             if factor not in seq_set:

%o                 seq.append(factor)

%o                 seq_set.add(factor)

%o                 done = True

%o                 break

%o print(seq) # _Robert C. Lyons_, Jan 01 2025

%Y Cf. A379652, A379649.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 31 2024