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.

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

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