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