OFFSET
1,1
COMMENTS
Prime terms from A273999.
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); ...
a(8) > 10^15. - Jacques Tramu, Sep 17 2018
a(9) > 1.7*10^18. - Giovanni Resta, Nov 12 2018
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
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Jun 06 2016
EXTENSIONS
a(8) from Giovanni Resta, Nov 12 2018
STATUS
approved