A079578 Least number coprime to n and greater than n+1.

3, 5, 5, 7, 7, 11, 9, 11, 11, 13, 13, 17, 15, 17, 17, 19, 19, 23, 21, 23, 23, 25, 25, 29, 27, 29, 29, 31, 31, 37, 33, 35, 35, 37, 37, 41, 39, 41, 41, 43, 43, 47, 45, 47, 47, 49, 49, 53, 51, 53, 53, 55, 55, 59, 57, 59, 59, 61, 61, 67, 63, 65, 65, 67, 67, 71, 69, 71, 71, 73, 73

Offset: 1

Author

Reinhard Zumkeller, Jan 24 2003

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053669, A116933, A116934, A249270.

Programs

Haskell

a079578 n = head [m | m <- [n + 2 ..], gcd m n == 1]
-- Reinhard Zumkeller, Oct 01 2014

Mathematica

a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; n + p]; Array[a, 100] (* Amiram Eldar, Apr 13 2025 *)

Formula

a(n) = n + A053669(n).

a(n) = (A116934(n) - n)/A116933(n). - Reinhard Zumkeller, Feb 27 2006

Sum_{k=1..n} a(k) ~ n^2 / 2 + c * n, where c = A249270. - Amiram Eldar, Apr 13 2025