OFFSET
1,1
COMMENTS
Equivalently, integers k == 5 (mod 6) such that 4^k == 4 (mod k) and 2^(k-1) == 4 (mod k-1).
Equivalently, integers k == 5 (mod 6) such that both k and (k-1)/2 are primes or (odd or even) Fermat 4-pseudoprimes (A122781).
Contains terms k of A175625 such that k == 5 (mod 6).
Contains terms k of A303448 such that k == 5 (mod 6).
Many composite terms of this sequence are of the form A007583(m) = (2^(2m+1) + 1)/3 (for m in A303009). It is unknown if there exist composite terms not of this form.
Numbers k such that 2^(k-1) == 3k+1 (mod 3(k-1)k). This sequence contains all safe primes except 7. The term a(20) = 683 = 2*341+1 is the smallest prime that is not safe. - Thomas Ordowski, Jun 07 2021
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[1, 3001, 2], PowerMod[4, #, 3#]==4&&PowerMod[2, #-1, 3(#-1)]==4&] (* Harvey P. Dale, Aug 04 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, Oct 27 2010
EXTENSIONS
Edited by Max Alekseyev, Apr 24 2018
STATUS
approved