login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A273871 Primes p such that (4^(p-1)-1) == 0 mod ((p-1)^2+1). 2
3, 5, 17, 257, 8209, 59141, 65537, 649801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime terms from A273870.

The first 5 known Fermat primes from A019434 are in this sequence.

Conjecture 1: also primes p such that ((4^k)^(p-1)-1) == 0 mod ((p-1)^2+1) for all k >= 0.

Conjecture 2: supersequence of Fermat primes (A019434).

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

5 is term because (4^(5-1)-1) == 0 mod ((5-1)^2+1); 255 == 0 mod 17.

PROG

(MAGMA) [n: n in [1..100000] | IsPrime(n) and (4^(n-1)-1) mod ((n-1)^2+1) eq 0]

(PARI) is(n)=isprime(n) && Mod(4, (n-1)^2+1)^(n-1)==1 \\ Charles R Greathouse IV, Jun 08 2016

CROSSREFS

Cf. A019434, A273870.

Sequence in context: A256510 A260377 A056130 * A078726 A019434 A164307

Adjacent sequences:  A273868 A273869 A273870 * A273872 A273873 A273874

KEYWORD

nonn,more

AUTHOR

Jaroslav Krizek, Jun 01 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)