|
|
A274000
|
|
Primes p of the form k^2 + 1 that divide 4^k - 1.
|
|
2
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The first 4 known Fermat primes > 3 from A019434 are in this sequence.
Conjecture: also primes p of the form n^2+1 such that divides (4^k)^n-1 for all k >= 0. Example: 17 = 4^2+1 is a term because divides (4^k)^4-1 for all k>=0: 0/17 = 0 (k=0); 255/17 = 15 (k=1); 65535/17 = 3855 (k=2); 16777215/17 = 986895 (k=3); 4294967295/17 = 252645135 (k=4); 1099511627775/17 = 64677154575 (k=5); ...
|
|
LINKS
|
|
|
EXAMPLE
|
17 = 4^2 + 1 is a term because it divides 4^4 - 1; 255/17 = 15.
|
|
PROG
|
(PARI) is(n) = ceil(sqrt(n-1))==sqrtint(n-1) && Mod(4, n)^(sqrtint(n))==1
for(n=0, 1e12, if(is(n^2+1), if(ispseudoprime(n^2+1), print1(n^2+1, ", ")))) \\ Felix Fröhlich, Jun 12 2016
|
|
CROSSREFS
|
Subsequence of A002496 (primes of the form n^2+1).
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|