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A354430
First diagonal of an array, generated from the sequence of the nonprimes.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Tamas Sandor Nagy, May 27 2022
EXTENSIONS
a(8) and beyond from Michael S. Branicky, May 28 2022
STATUS
approved