A376684 - OEIS

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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).

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..34.

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.

Cf. A002808, A064113, A065890, A173390, A233671, A258025, A333214, A333254, A376680, A377033, A377037.

Sequence in context: A034421 A353306 A211221 * A029448 A249179 A103014

Adjacent sequences: A376681 A376682 A376683 * A376685 A376686 A376688

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 15 2024

STATUS

approved