A359278 Antidiagonal sums of A354967.

1, 4, 9, 19, 45, 127, 491, 2597, 18905, 180253, 2176101, 32236029, 571516361, 11885151437, 285237145381, 7794999370341, 239867327549943, 8232788441242931, 312611538663794793, 13040004273788572983

Offset: 1

Author

Christoph B. Kassir, Feb 03 2023

Keywords

• nonn
• more

Crossrefs

Cf. A000040, A058009, A354967, A345669.

Programs

PARI

a(n) = sum(k=1, n, my(p=k); for(j=k+1, n, p=prime(p)); p) \\ Andrew Howroyd, Feb 04 2023

Python

from sympy import prime
def nprime(x, y):
    p = x
    for _ in range(y):
        p = prime(p)
    return p
def a(n):
    return sum([nprime(k, n-k) for k in range(1, n+1)])

Formula

a(n) = Sum_{k=1..n} p(k, n-k+1), where p(n,0) = n and p(n,k) = prime(p(n, k-1)) for k >= 1.

Extensions

a(9)-a(15) from Andrew Howroyd, Feb 03 2023

a(16)-a(20) from Alois P. Heinz, Feb 03 2023