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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
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Mar 10 2010
EXTENSIONS
Terms from a(22) onwards corrected by Ivan Neretin, Dec 04 2018
STATUS
approved