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.
a(10)=67 corresponds to the prime number (67^1024 + 57^1024)/2, the smallest prime number of the form (A^1024 + B^1024)/2 (or more precisely, it minimizes A).
Table[a=1; While[Or@@PrimeQ[Table[(a^(2^n)+b^(2^n))/2,{b,a++}]]==False];a,{n,0,9}] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
for(n=0, 30, forstep(a=3, +oo, 2, forstep(b=1, a-2, 2, if(ispseudoprime((a^(2^n)+b^(2^n))/2), print1(a, ", "); next(3)))))
from sympy import isprime
def a(n):
A, p, Ap = 3, 2**n, 3**(2**n)
while True:
if any(isprime((Ap + B**p)//2) for B in range(1, A, 2)): return A
A += 2; Ap = A**p
print([a(n) for n in range(10)]) # Michael S. Branicky, Mar 03 2021
a(10)=663 corresponds to the prime (663^1024 + 661^1024)/2.
lst = {}; For[n=0, n<=14, n++, k=3; While[! PrimeQ[(k^(2^n) + (k-2)^(2^n))/2], k++]; AppendTo[lst, k]]; lst (* Robert Price, Apr 29 2018 *)
for(n=0,20,forstep(k=3,+oo,2,if(ispseudoprime((k^(2^n)+(k-2)^(2^n))/2),print1(k,", ");break())))
For n=5, the six numbers 2669 + 720, 2669^2 + 720^2, 2669^4 + 720^4, 2669^8 + 720^8, 2669^16 + 720^16, and 2669^32 + 720^32 are all prime, and (A,B) = (2669,720) is the least pair with this property, so a(5)=2669. For n=6, (A,B) = (34559,29000). For n=7, (A,B) = (26507494,6329559). For n=8, (A,B) = (3242781025,1554825312).
a(n)=for(A=1, oo, for(B=1, A-1, for(k=0, n, !ispseudoprime(A^(2^k)+B^(2^k)) && next(2)); return(A)))
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