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

1,3

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

E. Labos, Graph of first 50000 terms

Formula

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

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 *)

Prog

(PARI) for(n=1, 100, print1(prime(n)%n, ", "))
(Magma) [(NthPrime(n) mod n): n in [1..100]]; // Vincenzo Librandi, Apr 06 2011
(Haskell)
a004648 n = a004648_list !! (n-1)
a004648_list = zipWith mod a000040_list [1..]
-- Reinhard Zumkeller, Jul 30 2012
(SageMath)
def A004648(n): return (nth_prime(n)%n)
[A004648(n) for n in range(1, 101)] # G. C. Greubel, Apr 20 2023

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.

Sequence in context: A123185 A133569 A141071 * A265848 A139438 A377842

Adjacent sequences: A004645 A004646 A004647 * A004649 A004650 A004651

Keyword

nonn

Author

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

Extensions

More terms from Clark Kimberling

Corrected by Jaroslav Krizek, Dec 16 2009

Status

approved