A174162 a(1) = 2. Let k >= 1 be the minimal integer such that 2*k*a(n-1) + 1 has at least one prime divisor which is not already in the sequence. Then a(n) is the smallest such divisor.

2, 5, 11, 23, 47, 19, 3, 7, 29, 59, 17, 103, 619, 2477, 991, 661, 3967, 2267, 907, 191, 383, 13, 53, 107, 43, 173, 347, 139, 31, 83, 167, 67, 269, 359, 719, 1439, 2879, 443, 887, 71, 61, 41, 137, 823, 37, 149, 199, 797, 1063, 709, 2837, 227, 101, 607, 3643, 21859

Offset

1,1

Comments

Conjectures: 1) The sequence is a permutation of prime numbers; 2) k = k(n) runs all positive integers.

Links

Table of n, a(n) for n=1..56.

Mathematica

a = {2}; Do[k = 1; While[(d = Complement[FactorInteger[2 k a[[-1]] + 1][[All, 1]], a]) == {}, k++]; AppendTo[a, Min@d], {n, 50}]; a (* Jinyuan Wang, Feb 26 2020 *)

Crossrefs

Cf. A005132, A063733, A078943, A174161.

Sequence in context: A075712 A349411 A347309 * A379652 A340799 A186253

Adjacent sequences: A174159 A174160 A174161 * A174163 A174164 A174165

Keyword

nonn

Author

Vladimir Shevelev, Mar 10 2010

Extensions

More terms from Jinyuan Wang, Feb 26 2020

Status

approved