A144291 Triangular numbers n*(n-1)/2 with n and n -1 nonprime.

0, 36, 45, 105, 120, 210, 231, 300, 325, 351, 378, 528, 561, 595, 630, 741, 780, 990, 1035, 1176, 1225, 1275, 1326, 1485, 1540, 1596, 1653, 1953, 2016, 2080, 2145, 2346, 2415, 2775, 2850, 2926, 3003, 3240, 3321, 3570, 3655, 3741, 3828, 4095, 4186, 4278

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 01 2008

Keywords

• nonn

Examples

			If n=1, then 1*(1-1)/2=0=a(1).
If n=9, then 9*(9-1)/2=36=a(2).
etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A068780, A141468.

Programs

Maple

p:= -1: Res:= NULL: count:= 0:
while count < 100 do
  q:= p; p:= nextprime(p);
  if p - q > 2 then
    count:= count + p-q-2;
    Res:= Res, seq(k*(k+1)/2, k=q+1..p-2);
  fi
od:
Res; # Robert Israel, Jul 03 2018

Mathematica

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 *)

Formula

a(n) = A000217(A068780(n-1)), n>1. - R. J. Mathar, Dec 10 2008

Extensions

3570 inserted by R. J. Mathar, Dec 10 2008