A181356
Smallest k such that 2^(2^n) - k is a safe prime.
Original entry on oeis.org
5, 29, 269, 209, 1469, 15449, 36113, 38117, 1093337, 1942289, 10895177, 43644929, 364486013, 718982153, 2356107437
Offset: 2
a(2)=5 because 2^(2^2) - 5 = 11 is the largest safe prime less than 16.
A140331
Smallest k such that 3^(3^n) - k is prime.
Original entry on oeis.org
1, 4, 2, 26, 10, 466, 506, 128, 13342, 5974, 8410, 6470
Offset: 0
a(4) = 10 because 3^(3^4) - 10 = 443426488243037769948249630619149892793 is prime.
A364452
Smallest k such that 4^(4^n) - k is prime.
Original entry on oeis.org
1, 5, 5, 159, 569, 1557, 2439, 25353, 24317, 164073
Offset: 0
a(2) = 5 because 4^(4^2) - 5 = 4294967291 is prime.
-
lst={};Do[Do[p=4^(4^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[4^(4^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 4^(4^n)}, x - NextPrime[x, -1]]; Array[y, 7]
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a(n) = my(x = 4^(4^n)); x - precprime(x);
A364453
Smallest k such that 5^(5^n) - k is prime.
Original entry on oeis.org
2, 4, 64, 124, 228, 10978, 73738, 66346
Offset: 0
a(2) = 64 because 5^(5^2) - 64 = 298023223876953061 is prime.
-
lst={};Do[Do[p=5^(5^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[5^(5^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 5^(5^n)}, x - NextPrime[x, -1]]; Array[y, 7]
-
a(n) = my(x = 5^(5^n)); x - precprime(x);
A364454
Smallest k such that 6^(6^n) - k is prime.
Original entry on oeis.org
1, 7, 35, 587, 629, 1819, 106843
Offset: 0
a(2) = 35 because 6^(6^2) - 35 = 10314424798490535546171949021 is prime.
-
lst={};Do[Do[p=6^(6^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[6^(6^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 6^(6^n)}, x - NextPrime[x, -1]]; Array[y, 7]
-
a(n) = my(x = 6^(6^n)); x - precprime(x);
A360080
Smallest k such that 2^(2^n) + k is a safe prime.
Original entry on oeis.org
1, 7, 7, 7, 91, 3103, 12451, 230191, 286867, 1657867, 10029811, 29761351, 22410151, 98402791, 167137543
Offset: 1
a(3) = 7 because 2^(2^3) + 7 = 263 is the smallest safe prime greater than 256.
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a(n) = {my(k=1); pow2 = 2^(2^n); while (!(isprime(pow2 + k) && isprime((pow2 + k - 1)/2)), k+=2); k;} \\
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from sympy import isprime, nextprime
def A360080(n):
if n <= 1: return 1
m = 1<<(1<Chai Wah Wu, Jan 27 2023
A058221
Next-to-smallest k such that 2^(2^n) - k is prime.
Original entry on oeis.org
2, 5, 15, 17, 17, 83, 173, 357, 629, 179, 2543, 8067, 5619, 29027, 38783, 99267
Offset: 1
A382666
Smallest k such that 7^(7^n) - k is prime.
Original entry on oeis.org
2, 2, 6, 512, 3918, 48966
Offset: 0
a(2) = 6 because 7^(7^2) - 6 = 256923577521058878088611477224235621321601 is prime.
-
lst={};Do[Do[p=7^(7^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[7^(7^n)-k],Break[]];k++];k],k],{n,0,7}]
y[n_] := Module[{x = 7^(7^n)}, x - NextPrime[x, -1]]; Array[y, 7]
-
a(n) = my(x = 7^(7^n)); x - precprime(x-1);
-
from sympy import prevprime
def a(n):
base = 7**(7**n)
return base - prevprime(base)
# Jakub Buczak, May 04 2025
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