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

1,2

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.

Links

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

Example

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 ...

Prog

(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

Crossrefs

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

Sequence in context: A213585 A308579 A246831 * A122238 A101289 A085287

Adjacent sequences: A354427 A354428 A354429 * A354431 A354432 A354433

Keyword

nonn,easy

Author

Tamas Sandor Nagy, May 27 2022

Extensions

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

Status

approved