A004648 a(n) = prime(n) mod n.

0, 1, 2, 3, 1, 1, 3, 3, 5, 9, 9, 1, 2, 1, 2, 5, 8, 7, 10, 11, 10, 13, 14, 17, 22, 23, 22, 23, 22, 23, 3, 3, 5, 3, 9, 7, 9, 11, 11, 13, 15, 13, 19, 17, 17, 15, 23, 31, 31, 29, 29, 31, 29, 35, 37, 39, 41, 39, 41, 41, 39, 45, 55, 55, 53, 53, 63, 65, 2, 69, 69, 71, 2, 3, 4, 3

Offset: 1

Author

N. J. A. Sloane, Daniel Wild (wild(AT)edumath.u-strasbg.fr)

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• Labos Elemer, Graph of first 50000 terms

Crossrefs

1's occur at A023143, 2's at A023144, 3's at A023145, 4's at A023146, 5's at A023147, 6's at A023148, 7's at A023149, 8's at A023150, 9's at A023151, 10's at A023152, == -1's at A045924.

For records see A127149, A127150.

Programs

Haskell

a004648 n = a004648_list !! (n-1)
a004648_list = zipWith mod a000040_list [1..]
-- Reinhard Zumkeller, Jul 30 2012

Magma

[(NthPrime(n) mod n): n in [1..100]]; // Vincenzo Librandi, Apr 06 2011

Maple

A004648 := proc(n)
    modp(ithprime(n),n) ;
end proc: # R. J. Mathar, Dec 02 2014

Mathematica

Table[Mod[Prime[n], n], {n, 100}] (* Zak Seidov, Apr 25 2005 *)

PARI

for(n=1,100,print1(prime(n)%n,","))

Python

from sympy import prime; print([prime(i) % i for i in range(1, 101)]) # Jwalin Bhatt, Jul 29 2025

SageMath

def A004648(n): return (nth_prime(n)%n)
[A004648(n) for n in range(1,101)] # G. C. Greubel, Apr 20 2023

Formula

a(n) = prime(n) - n*floor(prime(n)/n)

Extensions

More terms from Clark Kimberling

Corrected by Jaroslav Krizek, Dec 16 2009