%I #27 Jul 23 2022 19:23:50
%S 1,7,22,58,142,334,766,1726,3837,8435,18364,39646,84986,181117,384160,
%T 811676,1709425,3590213,7522354,15728427,32827027,68405533,142344708,
%U 295824870,614046159,1273068141,2636250146,5452584131,11264148401,23242423457,47903544728
%N First diagonal of an array, generated from the sequence of the nonprimes.
%C Mirroring the idea in A048457, here with nonprimes, and including 1 of the first generation.
%C We write down the sequence of the nonprimes 1, 4, 6, ... in the first row of the array. Nonprime(k) + nonprime(k+2) will generate the second row. Thereafter we generate the further rows in a similar manner. The leftmost diagonal gives the sequence.
%H Michael S. Branicky, <a href="/A354430/b354430.txt">Table of n, a(n) for n = 1..3311</a>
%e 1 4 6 8 9 10 12 14 15 16 18 20 21 ...
%e 7 12 15 18 21 24 27 30 33 36 39 ...
%e 22 30 36 42 48 54 60 66 72 ...
%e 58 72 84 96 108 120 132 ...
%e 142 168 192 216 240 ...
%e 334 384 432 ...
%e 766 ...
%o (Python)
%o from sympy import composite
%o from functools import lru_cache
%o @lru_cache(maxsize=None)
%o def T(r, k):
%o if r == 1: return 1 if k == 1 else composite(k-1)
%o return T(r-1, k) + T(r-1, k+2)
%o def a(n): return T(n, 1)
%o print([a(n) for n in range(1, 30)]) # _Michael S. Branicky_, May 28 2022
%Y Cf. A001787, A018252, A048457, A048448, A099862.
%K nonn,easy
%O 1,2
%A _Tamas Sandor Nagy_, May 27 2022
%E a(8) and beyond from _Michael S. Branicky_, May 28 2022