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A376684
Antidiagonal-sums of the absolute value of the array A376682(n,k) = n-th term of the k-th differences of the noncomposite numbers (A008578).
8
1, 3, 4, 9, 12, 27, 50, 109, 224, 471, 942, 1773, 3118, 4957, 7038, 9373, 16256, 55461, 150622, 346763, 718972, 1377101, 2462220, 4114987, 6387718, 9112455, 12051830, 17160117, 40946860, 134463917, 349105370, 800713921, 1684145408, 3297536923, 6040907554
OFFSET
0,2
EXAMPLE
The fourth antidiagonal of A376682 is: (7, 2, 0, -1, -2), so a(4) = 12.
MATHEMATICA
nn=12;
t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1, !PrimeQ[#]&]&, 1, 2*nn], k], nn], {k, 0, nn}];
Total/@Table[Abs[t[[j, i-j+1]]], {i, nn}, {j, i}]
CROSSREFS
For the modern primes (A000040) we have A376681, absolute version of A140119.
For firsts instead of row-sums we have A030016, modern A007442.
These are the antidiagonal-sums of the absolute value of A376682 (modern A095195).
This is the absolute version of A376683.
For first zero-positions we have A376855, modern A376678.
A000040 lists the modern primes, differences A001223, seconds A036263.
A008578 lists the noncomposites, first differences A075526.
Sequence in context: A034421 A353306 A211221 * A029448 A249179 A103014
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 15 2024
STATUS
approved