

A139319


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. a(1)=1.


3



1, 1, 2, 3, 19, 5, 13, 7, 17, 29, 43, 11, 103, 41, 59, 31, 67, 53, 37, 79, 83, 109, 137, 23, 149, 181, 107, 139, 173, 89, 61, 127, 131, 101, 349, 71, 73, 113, 233, 199, 163, 167, 257, 263, 179, 229, 281, 47, 97, 449, 509, 311, 211, 269, 439, 223, 227, 347
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OFFSET

1,3


COMMENTS

Are there any composites in this sequence? If not, is this sequence, with the exception of terms a(1) and a(2), 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(10) we check: 10*1  1= 9, which is not coprime to a(4)=3. 10*2  1= 19, which is not coprime to a(5)=19. But 10*3  1 = 29, which is coprime to terms a(1) through a(9). So a(10) = 29.


MATHEMATICA

Fold[Append[#1, SelectFirst[#2 Range@ 120  1, Function[k, CoprimeQ @@ Append[#1, k]]]] &, {1}, Range[2, 58]] (* Michael De Vlieger, Oct 22 2017 *)


CROSSREFS

Cf. A139317, A139320.
Sequence in context: A230602 A269343 A292991 * A269251 A092925 A082012
Adjacent sequences: A139316 A139317 A139318 * A139320 A139321 A139322


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 13 2008


STATUS

approved



