This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359278 #30 Feb 18 2023 21:22:29
%S A359278 1,4,9,19,45,127,491,2597,18905,180253,2176101,32236029,571516361,
%T A359278 11885151437,285237145381,7794999370341,239867327549943,
%U A359278 8232788441242931,312611538663794793,13040004273788572983
%N A359278 Antidiagonal sums of A354967.
%F A359278 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.
%o A359278 (Python)
%o A359278 from sympy import prime
%o A359278 def nprime(x, y):
%o A359278 p = x
%o A359278 for _ in range(y):
%o A359278 p = prime(p)
%o A359278 return p
%o A359278 def a(n):
%o A359278 return sum([nprime(k, n-k) for k in range(1, n+1)])
%o A359278 (PARI) a(n) = sum(k=1, n, my(p=k); for(j=k+1, n, p=prime(p)); p) \\ _Andrew Howroyd_, Feb 04 2023
%Y A359278 Cf. A000040, A058009, A354967, A345669.
%K A359278 nonn,more
%O A359278 1,2
%A A359278 _Christoph B. Kassir_, Feb 03 2023
%E A359278 a(9)-a(15) from _Andrew Howroyd_, Feb 03 2023
%E A359278 a(16)-a(20) from _Alois P. Heinz_, Feb 03 2023