A376681 Row sums of the absolute value of the array A095195(n, k) = n-th term of the k-th differences of the prime numbers (A000040).

2, 4, 8, 10, 22, 36, 72, 134, 266, 500, 874, 1418, 2044, 2736, 4626, 15176, 41460, 95286, 196368, 372808, 660134, 1092790, 1682198, 2384724, 3147706, 4526812, 11037090, 36046768, 93563398, 214796426, 452129242, 885186658, 1619323680, 2763448574, 4368014812

Offset: 1

Author

Gus Wiseman, Oct 15 2024

Keywords

• nonn

Examples

			The fourth row of A095195 is: (7, 2, 0, -1), so a(4) = 10.
		

Crossrefs

For firsts instead of row-sums we have A007442 (modern version of A030016).

This is the absolute version of A140119.

If 1 is considered prime (A008578) we get A376684, absolute version of A376683.

For first zero-positions we have A376678 (modern version of A376855).

For composite instead of prime we have A377035.

For squarefree instead of prime we have A377040, nonsquarefree A377048.

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

A008578 lists the noncomposites, differences A075526, seconds A036263 with 0 prepended.

Cf. A064113, A065890, A084758, A173390, A233671, A258025, A333214, A333254, A376602, A376651, A376652, A377033.

Programs

Mathematica

nn=15;
t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1,!PrimeQ[#]&]&,2,2*nn],k],nn],{k,0,nn}]
Total/@Abs/@Table[t[[j,i-j+1]],{i,nn},{j,i}]

Extensions

More terms from Pontus von Brömssen, Oct 17 2024