A352255 Write down the prime numbers 2,3,5,... and write below each one the preceding nonprimes greater than the previous prime, in decreasing order. Sums of the antidiagonals give the terms of the sequence.

2, 4, 5, 11, 17, 23, 38, 43, 56, 65, 80, 114, 103, 143, 186, 170, 188, 214, 234, 242, 311, 338, 292, 310, 342, 439, 458, 487, 490, 418, 434, 458, 502, 528, 673, 555, 708, 717, 748, 916, 1089, 1263, 1132, 982, 921, 757, 791, 813, 843, 1068, 1296, 1302, 1133, 1379, 1162

Offset

1,1

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

a(4) = 4 + 7 = 11;
a(7) = 9 + 12 + 17 = 38.
The initial table for calculating the terms of the sequence is shown below. The terms are the sums of numbers on the antidiagonals.
.
Antidiagonal sums: 2  4  5 11 17 23 38 43 56 65
                  /  /  /  /  /  /  /  /  /  /
                 /  /  /  /  /  /  /  /  /  /
        primes: 2  3  5  7 11 13 17 19 23 29 ...
                | /   | /| /| /| /| /| /| /|
                |/    |/ |/ |/ |/ |/ |/ |/ |
                1     4  6 10 12 16 18 22 28 ...
                            | /  /| /  /| /|
                            |/  / |/  / |/ |
                            9  / 15  / 21 27 ...
                            | /   | /   | /|
                            |/    |/    |/ |
                            8    14    20 26 ...
                                           |
                                           |
                                          25 ...
                                           |
                                           |
                                          24 ...

Prog

(MATLAB)
function a = A352255( max_p )
    p = primes(max_p);
    a = zeros(1, length(p));
    while sum(p) > 0
        a = a+p;
        p = [0 p(1:end-1)];
        p = p-1;
        p(p<0) = 0;
        p(isprime(p)) = 0;
    end
end % Thomas Scheuerle, Mar 10 2022
(PARI) { for (n=1, #a=vector(55), m = n; forstep (v=prime(n), if (n==1, 1, prime(n-1)+1), -1, a[m]+=v; if (m++>#a, break)); print1 (a[n]", ")) } \\ Rémy Sigrist, Mar 12 2022

Crossrefs

Cf. A102370.

Sequence in context: A366702 A089416 A056817 * A192581 A095023 A049913

Adjacent sequences: A352252 A352253 A352254 * A352256 A352257 A352258

Keyword

nonn

Author

Tamas Sandor Nagy, Mar 09 2022

Status

approved