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

1,2

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

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A293170 A341469 A101200 * A057449 A308601 A286931

Adjacent sequences: A122582 A122583 A122584 * A122586 A122587 A122588

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 20 2006

Status

approved