A144291 - OEIS

%I #10 Mar 27 2019 09:53:20

%S 0,36,45,105,120,210,231,300,325,351,378,528,561,595,630,741,780,990,

%T 1035,1176,1225,1275,1326,1485,1540,1596,1653,1953,2016,2080,2145,

%U 2346,2415,2775,2850,2926,3003,3240,3321,3570,3655,3741,3828,4095,4186,4278

%N Triangular numbers n*(n-1)/2 with n and n -1 nonprime.

%H Robert Israel, <a href="/A144291/b144291.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000217(A068780(n-1)), n>1. - _R. J. Mathar_, Dec 10 2008

%e If n=1, then 1*(1-1)/2=0=a(1).

%e If n=9, then 9*(9-1)/2=36=a(2).

%e etc.

%p p:= -1: Res:= NULL: count:= 0:

%p while count < 100 do

%p   q:= p; p:= nextprime(p);

%p   if p - q > 2 then

%p     count:= count + p-q-2;

%p     Res:= Res, seq(k*(k+1)/2, k=q+1..p-2);

%p   fi

%p od:

%p Res; # _Robert Israel_, Jul 03 2018

%t Reap[For[n = 1, n <= 100, n++, If[!PrimeQ[n] && !PrimeQ[n-1], Sow[n(n-1)/2] ] ] ][[2, 1]] (* _Jean-François Alcover_, Mar 27 2019 *)

%Y Cf. A000040, A000217, A068780, A141468.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Dec 01 2008

%E 3570 inserted by _R. J. Mathar_, Dec 10 2008