A038702 - OEIS

%I #34 Feb 27 2018 18:03:43

%S 1,1,4,2,4,3,4,16,13,4,5,16,4,16,36,36,4,36,16,4,36,16,36,64,16,4,16,

%T 4,16,83,16,36,4,100,4,36,36,16,36,36,4,100,4,16,4,144,144,16,4,16,36,

%U 4,100,36,36,36,4,36,16,4,100,196,16,4

%N Prime(n)^2 mod prime(n-1).

%C a(n+1) = n-th prime gap squared mod the n-th prime = A076821(n) mod A000040(n). Probably a(n) = A076821(n+1) for n > 31. This holds up to 4 * 10^18. - _Charles R Greathouse IV_, Apr 17 2012

%H Vincenzo Librandi, <a href="/A038702/b038702.txt">Table of n, a(n) for n = 2..10000</a>

%e To get a(4): square the fourth prime to get 7^2 = 49. The remainder when this is divided by the third prime, 5, is 4. So a(3) = 4.

%p A038702 := proc(n)

%p     modp( ithprime(n)^2,ithprime(n-1)) ;

%p end proc: # _R. J. Mathar_, Jan 09 2015

%t Table[Mod[Prime[n+1]^2,Prime[n]],{n,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2010 *)

%t Table[PowerMod[Prime[n],2,Prime[n-1]],{n,2,70}] (* _Harvey P. Dale_, Mar 22 2012 *)

%o (PARI) a(n)=prime(n)^2%prime(n-1) \\ _Charles R Greathouse IV_, Apr 17 2012

%Y Cf. A038703.

%K nonn,easy

%O 2,3

%A _Neil Fernandez_, May 01 2000