A157419 a(0)=1. a(n) = the smallest integer coprime to a(n-1) and greater than the n-th prime.

1, 3, 4, 7, 8, 13, 14, 19, 20, 27, 31, 32, 39, 43, 44, 49, 54, 61, 62, 69, 73, 74, 81, 85, 91, 99, 103, 104, 109, 110, 117, 128, 133, 138, 143, 150, 157, 158, 165, 169, 174, 181, 182, 193, 194, 199, 200, 213, 224, 229, 230, 237, 241, 242, 255, 259, 264, 271, 272, 279

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Example

a(8) = 20, and the 9th prime is 23. So for a(9) we want the smallest integer that is both coprime to 20 and is > 23. Checking: 24 is not coprime to 20. 25 is not coprime to 20. 26 is not coprime to 20. But 27 is coprime to 20, so a(9) = 27.

Mathematica

Fold[Append[#1, Block[{k = Prime@ #2 + 1}, While[! CoprimeQ[k, #1[[-1]] ], k++]; k]] &, {1}, Range@ 59] (* Michael De Vlieger, Oct 30 2017 *)
sic[{n_, a_}]:=Module[{k=Prime[n+1]+1}, While[!CoprimeQ[a, k], k++]; {n+1, k}]; NestList[sic, {0, 1}, 60][[;; , 2]] (* Harvey P. Dale, Oct 22 2024 *)

Crossrefs

Cf. A157420, A157421.

Sequence in context: A338467 A284491 A284506 * A008368 A023054 A374962

Adjacent sequences: A157416 A157417 A157418 * A157420 A157421 A157422

Keyword

nonn

Author

Leroy Quet, Feb 28 2009

Extensions

Extended by Ray Chandler, Jun 19 2009

Status

approved