A376683 Antidiagonal-sums of the array A376682(n,k) = n-th term of the k-th differences of the noncomposite numbers (A008578).

1, 3, 4, 9, 6, 27, -20, 109, -182, 471, -868, 1737, -2872, 4345, -4700, 1133, 14060, -55275, 150462, -346093, 717040, -1369351, 2432872, -4002905, 5964846, -7524917, 6123130, 4900199, -40900410, 134309057, -348584552, 798958881, -1678213106, 3277459119

Offset: 0

Author

Gus Wiseman, Oct 15 2024

Keywords

• sign

Examples

			The fourth anti-diagonal of A376682 is: (7, 2, 0, -1, -2), so a(4) = 6.
		

Crossrefs

The modern version (for A000040 instead of A008578) is A140119.

The absolute version is A376681.

Antidiagonal-sums of A376682 (modern version A095195).

For composite instead of noncomposite we have A377033.

For squarefree instead of noncomposite we have A377038, nonsquarefree A377046.

A000040 lists the modern primes, differences A001223, second A036263.

A008578 lists the noncomposites, first differences A075526.

Cf. A007442, A030016, A064113, A065890, A002808, A173390, A233671, A333214, A333254, A376678, A376684, A376855.

Programs

Mathematica

nn=12;
t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,!PrimeQ[#]&]&,1,2*nn],k],nn],{k,0,nn}];
Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]