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[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, ", ")))
The n-value for which n^128 + 1 is prime (sequence A056994) is n = 120 (where n > 1 by definition). Thus a(1) = 120.
lnk[n_]:=Module[{k=n+1,n128=n^128},While[!PrimeQ[n128+k^128],k++];k]; Array[lnk,60] (* Harvey P. Dale, Apr 22 2018 *)
a(n)=for(k=n+1,10^4,if(isprime(k^128+n^128),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**128+n**128):
return k
for n in range(1, 100):
print(a(n), end=', ')
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