A218036 a(n) = (n+1) + (n+3/2)*H(n) - (H(n)^3)/2, where H(n) = A002024(n).

4, 6, 9, 8, 12, 16, 10, 15, 20, 25, 12, 18, 24, 30, 36, 14, 21, 28, 35, 42, 49, 16, 24, 32, 40, 48, 56, 64, 18, 27, 36, 45, 54, 63, 72, 81, 20, 30, 40, 50, 60, 70, 80, 90, 100, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

Offset: 1

Author

Michel Marcus, Oct 19 2012

Keywords

• nonn
• tabl

Comments

All terms are composite.

Examples

			Sequence can be seen as a triangle that begins:
   4;
   6,  9;
   8, 12, 16;
  10, 15, 20, 25;
  12, 18, 24, 30, 36;
  14, 21, 28, 35, 42, 49;
  16, 24, 32, 40, 48, 56, 64;
  ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3655 (Rows n=1..85 of triangle, flattened).
• Blake Ralston, Elemental Complete Composite Number Generators, The Fibonacci Quarterly, Volume 23, Number 2, May 1985, pp. 149-150.

Crossrefs

Cf. A002024.

Programs

Magma

/* As triangle */ [[n*k +n + k+1: k in [1..n]]: n in [1.. 20]]; // Vincenzo Librandi, Jan 27 2025

Mathematica

Table[(k+1)*(n+1),{n,1,11},{k,1,n}]//Flatten (* Stefano Spezia, Nov 23 2019 *)

Python

from math import isqrt
def A218036(n): return ((m:=isqrt((k:=n<<1)<<2)+1>>1)*(k+3-m**2)>>1)+n+1 # Chai Wah Wu, Jun 14 2025

Formula

a(n) = (A002024(n)+1)*(n+1-A002024(n)*(A002024(n)-1)/2).

As a triangle: T(n, k) = (k + 1)*(n + 1) with 1 <= k <= n. - Stefano Spezia, Nov 23 2019