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

%I A218036 #41 Jun 14 2025 19:26:10
%S A218036 4,6,9,8,12,16,10,15,20,25,12,18,24,30,36,14,21,28,35,42,49,16,24,32,
%T A218036 40,48,56,64,18,27,36,45,54,63,72,81,20,30,40,50,60,70,80,90,100,22,
%U A218036 33,44,55,66,77,88,99,110,121,24,36,48,60,72,84,96,108,120,132,144
%N A218036 a(n) = (n+1) + (n+3/2)*H(n) - (H(n)^3)/2, where H(n) = A002024(n).
%C A218036 All terms are composite.
%H A218036 Vincenzo Librandi, <a href="/A218036/b218036.txt">Table of n, a(n) for n = 1..3655</a> (Rows n=1..85 of triangle, flattened).
%H A218036 Blake Ralston, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/23-2/ralston.pdf">Elemental Complete Composite Number Generators</a>, The Fibonacci Quarterly, Volume 23, Number 2, May 1985, pp. 149-150.
%F A218036 a(n) = (A002024(n)+1)*(n+1-A002024(n)*(A002024(n)-1)/2).
%F A218036 As a triangle: T(n, k) = (k + 1)*(n + 1) with 1 <= k <= n. - _Stefano Spezia_, Nov 23 2019
%e A218036 Sequence can be seen as a triangle that begins:
%e A218036    4;
%e A218036    6,  9;
%e A218036    8, 12, 16;
%e A218036   10, 15, 20, 25;
%e A218036   12, 18, 24, 30, 36;
%e A218036   14, 21, 28, 35, 42, 49;
%e A218036   16, 24, 32, 40, 48, 56, 64;
%e A218036   ...
%t A218036 Table[(k+1)*(n+1),{n,1,11},{k,1,n}]//Flatten (* _Stefano Spezia_, Nov 23 2019 *)
%o A218036 (Magma) /* As triangle */ [[n*k +n + k+1: k in [1..n]]: n in [1.. 20]]; // _Vincenzo Librandi_, Jan 27 2025
%o A218036 (Python)
%o A218036 from math import isqrt
%o A218036 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
%Y A218036 Cf. A002024.
%K A218036 nonn,tabl
%O A218036 1,1
%A A218036 _Michel Marcus_, Oct 19 2012