A122585 Reciprocal of n modulo smallest prime greater than n.

1, 2, 2, 4, 3, 6, 8, 7, 5, 10, 6, 12, 4, 11, 8, 16, 9, 18, 17, 15, 11, 22, 24, 23, 7, 19, 14, 28, 15, 30, 6, 22, 9, 12, 18, 36, 10, 27, 20, 40, 21, 42, 35, 31, 23, 46, 44, 21, 13, 35, 26, 52, 49, 47, 44, 39, 29, 58, 30, 60, 11, 40, 50, 22, 33, 66, 53, 47, 35, 70, 36, 72, 13, 63, 59

Offset: 1

Author

Franklin T. Adams-Watters, Oct 20 2006

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
• Eric Weisstein's World of Mathematics, Modular Inverse

Crossrefs

Cf. A006093, A040976, A124223, A151800, A362254.

Programs

Maple

a:= n-> n&^(-1) mod nextprime(n):
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 13 2023

Mathematica

Table[PowerMod[n,-1,NextPrime[n]],{n,80}] (* Harvey P. Dale, Apr 13 2023 *)

Python

from sympy import nextprime
def A122585(n): return pow(n,-1,nextprime(n)) # Chai Wah Wu, Apr 13 2023

Formula

From Alois P. Heinz, Apr 13 2023: (Start)

a(n) = n <=> n in { A006093 }.

a(n) = (n+1)/2 <=> n in { A040976 } \ { 0 }. (End)