OFFSET
0,2
COMMENTS
Row k of the array is the k-th differences of A000961.
FORMULA
A(i,j) = Sum_{k=0..j} (-1)^(j-k)*binomial(j,k)*A000961(i+k).
EXAMPLE
Array form:
n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8: n=9:
----------------------------------------------------------
k=0: 1 2 3 4 5 7 8 9 11
k=1: 1 1 1 1 2 1 1 2 2
k=2: 0 0 0 1 -1 0 1 0 1
k=3: 0 0 1 -2 1 1 -1 1 -3
k=4: 0 1 -3 3 0 -2 2 -4 6
k=5: 1 -4 6 -3 -2 4 -6 10 -8
k=6: -5 10 -9 1 6 -10 16 -18 5
k=7: 15 -19 10 5 -16 26 -34 23 9
k=8: -34 29 -5 -21 42 -60 57 -14 -42
k=9: 63 -34 -16 63 -102 117 -71 -28 104
Triangle form:
1
2 1
3 1 0
4 1 0 0
5 1 0 0 0
7 2 1 1 1 1
8 1 -1 -2 -3 -4 -5
9 1 0 1 3 6 10 15
11 2 1 1 0 -3 -9 -19 -34
13 2 0 -1 -2 -2 1 10 29 63
16 3 1 1 2 4 6 5 -5 -34 -97
MATHEMATICA
nn=12;
t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1, !PrimePowerQ[#]&]&, 1, 2*nn], k], nn], {k, 0, nn}]
Table[t[[j, i-j+1]], {i, nn}, {j, i}]
KEYWORD
AUTHOR
Gus Wiseman, Oct 20 2024
STATUS
approved