OFFSET
0,1
COMMENTS
Row n is the k-th differences of A002808 = the composite numbers.
FORMULA
A(i,j) = sum_{k=0..j} (-1)^(j-k) binomial(j,k) A002808(i+k).
EXAMPLE
Array begins:
n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8: n=9:
----------------------------------------------------------
k=0: 4 6 8 9 10 12 14 15 16
k=1: 2 2 1 1 2 2 1 1 2
k=2: 0 -1 0 1 0 -1 0 1 0
k=3: -1 1 1 -1 -1 1 1 -1 -1
k=4: 2 0 -2 0 2 0 -2 0 2
k=5: -2 -2 2 2 -2 -2 2 2 -2
k=6: 0 4 0 -4 0 4 0 -4 -1
k=7: 4 -4 -4 4 4 -4 -4 3 10
k=8: -8 0 8 0 -8 0 7 7 -29
k=9: 8 8 -8 -8 8 7 0 -36 63
Triangle begins:
4
6 2
8 2 0
9 1 -1 -1
10 1 0 1 2
12 2 1 1 0 -2
14 2 0 -1 -2 -2 0
15 1 -1 -1 0 2 4 4
16 1 0 1 2 2 0 -4 -8
18 2 1 1 0 -2 -4 -4 0 8
20 2 0 -1 -2 -2 0 4 8 8 0
21 1 -1 -1 0 2 4 4 0 -8 -16 -16
MATHEMATICA
nn=9;
t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1, PrimeQ]&, 4, 2*nn], k], nn], {k, 0, nn}]
CROSSREFS
First position of 0 in each row is A377037.
Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
KEYWORD
sign,tabl
AUTHOR
Gus Wiseman, Oct 17 2024
STATUS
approved