A004648 - OEIS

%I #32 Apr 21 2023 02:12:05

%S 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,

%T 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,

%U 37,39,41,39,41,41,39,45,55,55,53,53,63,65,2,69,69,71,2,3,4,3

%N a(n) = prime(n) mod n.

%H N. J. A. Sloane, <a href="/A004648/b004648.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Labos, <a href="/A004648/a004648.gif">Graph of first 50000 terms</a>

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

%p A004648 := proc(n)

%p     modp(ithprime(n),n) ;

%p end proc: # _R. J. Mathar_, Dec 02 2014

%t Table[Mod[Prime[n], n], {n, 100}] (* _Zak Seidov_, Apr 25 2005 *)

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

%o (Magma) [(NthPrime(n) mod n): n in [1..100]]; // _Vincenzo Librandi_, Apr 06 2011

%o (Haskell)

%o a004648 n = a004648_list !! (n-1)

%o a004648_list = zipWith mod a000040_list [1..]

%o -- _Reinhard Zumkeller_, Jul 30 2012

%o (SageMath)

%o def A004648(n): return (nth_prime(n)%n)

%o [A004648(n) for n in range(1,101)] # _G. C. Greubel_, Apr 20 2023

%Y 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.

%Y For records see A127149, A127150.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Daniel Wild (wild(AT)edumath.u-strasbg.fr)

%E More terms from _Clark Kimberling_

%E Corrected by _Jaroslav Krizek_, Dec 16 2009