A377035 Antidiagonal-sums of the absolute value of the array A377033(n,k) = n-th term of the k-th differences of the composite numbers (A002808).

4, 8, 10, 12, 14, 18, 21, 28, 34, 40, 47, 74, 96, 110, 138, 286, 715, 2393, 8200, 25731, 72468, 184716, 431575, 934511, 1892267, 3605315, 6494464, 11116110, 18134549, 28348908, 42701927, 62290660, 88313069, 120999433, 159769475, 221775851, 483797879

Offset: 1

Author

Gus Wiseman, Oct 18 2024

Keywords

• nonn

Examples

			The fourth antidiagonal of A377033 is (9, 1, -1, -1), so a(4) = 12.
		

Crossrefs

The version for prime instead of composite is A376681, absolute version of A140119.

The version for noncomposite is A376684, absolute version of A376683.

This is the antidiagonal-sums of absolute value of the array A377033.

For squarefree instead of composite we have A377040, absolute version of A377039.

For nonsquarefree instead of composite we have A377048, absolute version of A377047.

For prime-power instead of composite we have A377053, absolute version of A377052.

Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).

A000040 lists the primes, differences A001223, seconds A036263.

A002808 lists the composite numbers, differences A073783, seconds A073445.

A008578 lists the noncomposites, differences A075526.

Cf. A018252, A065310, A065890, A333254, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680, A377036.

Programs

Mathematica

q=Select[Range[120],CompositeQ];
t=Table[Sum[(-1)^(j-k)*Binomial[j,k]*q[[i+k]],{k,0,j}],{j,0,Length[q]/2},{i,Length[q]/2}];
Total/@Table[Abs[t[[j,i-j+1]]],{i,Length[q]/2},{j,i}]