A354430 First diagonal of an array, generated from the sequence of the nonprimes.

1, 7, 22, 58, 142, 334, 766, 1726, 3837, 8435, 18364, 39646, 84986, 181117, 384160, 811676, 1709425, 3590213, 7522354, 15728427, 32827027, 68405533, 142344708, 295824870, 614046159, 1273068141, 2636250146, 5452584131, 11264148401, 23242423457, 47903544728

Offset: 1

Author

Tamas Sandor Nagy, May 27 2022

Keywords

• nonn
• easy

Comments

Mirroring the idea in A048457, here with nonprimes, and including 1 of the first generation.

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.

Examples

			1    4    6    8    9   10   12   14   15   16   18   20   21 ...
     7   12   15   18   21   24   27   30   33   36   39 ...
         22   30   36   42   48   54   60   66   72 ...
              58   72   84   96  108  120  132 ...
                  142  168  192  216  240 ...
                       334  384  432 ...
                            766 ...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..3311

Crossrefs

Cf. A001787, A018252, A048457, A048448, A099862.

Programs

Python

from sympy import composite
from functools import lru_cache
@lru_cache(maxsize=None)
def T(r, k):
    if r == 1: return 1 if k == 1 else composite(k-1)
    return T(r-1, k) + T(r-1, k+2)
def a(n): return T(n, 1)
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, May 28 2022

Extensions

a(8) and beyond from Michael S. Branicky, May 28 2022