A174161 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, 3, 5, 19, 37, 73, 29, 23, 7, 13, 17, 11, 43, 257, 79, 157, 313, 139, 277, 41, 163, 31, 61, 487, 59, 47, 281, 1123, 449, 359, 239, 53, 211, 421, 101, 67, 89, 71, 283, 113, 677, 2707, 5413, 433, 173, 691, 1381, 251, 167, 1669, 5563, 7417, 44501, 431, 1723, 2297

Offset

1,1

Comments

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

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

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 (* Ivan Neretin, Dec 04 2018 *)

Crossrefs

Cf. A005132, A063733, A078943, A174162.

Sequence in context: A215316 A215308 A215104 * A072532 A215373 A359939

Adjacent sequences: A174158 A174159 A174160 * A174162 A174163 A174164

Keyword

nonn,uned

Author

Vladimir Shevelev, Mar 10 2010

Extensions

Terms from a(22) onwards corrected by Ivan Neretin, Dec 04 2018

Status

approved