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 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 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

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