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.
Select[Range[7000], PrimeQ[#^128 + (# + 1)^128] &]
Select[Range[5000], PrimeQ[#^256 + (# + 1)^256] &];
Select[Range[0, 4000], PrimeQ[#^512 + (# + 1)^512] &] Position[Partition[Range[3800]^512,2,1],?(PrimeQ[Total[#]]&)]//Flatten (* _Harvey P. Dale, Aug 03 2024 *)
[n: n in [1..10000] |IsPrime(n^1024 + (n+1)^1024)]
Select[Range[1, 10000], PrimeQ[#^1024 + (#+1)^1024] &]
for(n=1, 10000, if(isprime(n^1024 + (n+1)^1024), print1(n, ", ")))
[n: n in [1..10000] |IsPrime(n^2048 + (n+1)^2048)];
Select[Range[1, 10000], PrimeQ[#^2048 + (#+1)^2048] &]
for(n=1, 10000, if(isprime(n^2048 + (n+1)^2048), print1(n, ", ")))
[n: n in [1..10000] |IsPrime(n^4096 + (n+1)^4096)];
Select[Range[1, 10000], PrimeQ[#^4096 + (#+1)^4096] &]
for(n=1, 10000, if(isprime(n^4096 + (n+1)^4096), print1(n, ", ")))
[n: n in [1..10000] |IsPrime(n^8192 + (n+1)^8192)]
Select[Range[1, 10000], PrimeQ[#^8192 + (#+1)^8192] &]
for(n=1, 10000, if(isprime(n^8192 + (n+1)^8192), print1(n, ", ")))
8^64 + 11^64 = 4457915690803004131256192897205630962697827851093882159977969339137 is prime. Since 8^64 + 10^64 and 8^64 + 9^64 are both composite, a(8) = 11.
a(n)=for(k=n+1,10^4,if(isprime(k^64+n^64),return(k))) n=1;while(n<100,print1(a(n),", ");n++)
import sympy
from sympy import isprime
def a(n):
for k in range(n+1,10**4):
if isprime(k**64+n**64):
return k
n = 1
while n < 100:
print(a(n),end=', ')
n += 1
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