login
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).
9
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
1,1
EXAMPLE
The fourth row of A095195 is: (7, 2, 0, -1), so a(4) = 10.
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}]
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.
Sequence in context: A127101 A308832 A124849 * A056654 A365002 A370663
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 15 2024
EXTENSIONS
More terms from Pontus von Brömssen, Oct 17 2024
STATUS
approved