

A139317


a(n) = the smallest value of the form n*k + 1, k = positive integer, that is coprime to all the previous terms of this sequence.


3



2, 3, 7, 5, 11, 13, 29, 17, 19, 31, 23, 37, 53, 43, 61, 97, 103, 73, 191, 41, 127, 67, 47, 193, 101, 79, 109, 113, 59, 151, 311, 257, 199, 137, 71, 181, 149, 229, 157, 241, 83, 211, 173, 89, 271, 139, 283, 337, 197, 251, 307, 313, 107, 163, 331, 281
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OFFSET

1,1


COMMENTS

Are there any composites in this sequence? If not, is this sequence a permutation of the primes?


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1000 (first 100 terms from Andrew V. Sutherland)
Andrew V. Sutherland, Comments on A139317 and A139319


EXAMPLE

For a(7) we check: 7*1 +1= 8, which is not coprime to a(1)=2. 7*2 +1= 15, which is not coprime to either a(2)=3 or to a(4)=5. 7*3 +1 = 22, which is not coprime to either a(1)=2 or to a(5)=11. But 7*4+1 = 29, which is coprime to terms a(1) through a(6). So a(7) = 29.


MATHEMATICA

Fold[Append[#1, SelectFirst[#2 Range@ 120 + 1, Function[k, CoprimeQ @@ Append[#1, k]]]] &, {2}, Range[2, 56]] (* Michael De Vlieger, Oct 22 2017 *)


CROSSREFS

Cf. A139318, A139319.
Sequence in context: A063904 A297929 A221858 * A117928 A333086 A064011
Adjacent sequences: A139314 A139315 A139316 * A139318 A139319 A139320


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 13 2008


STATUS

approved



