|
|
A273870
|
|
Numbers m such that 4^(m-1) == 1 (mod (m-1)^2 + 1).
|
|
2
|
|
|
1, 3, 5, 17, 217, 257, 387, 8209, 20137, 37025, 59141, 65537, 283801, 649801, 1382401, 373164545, 535019101, 2453039425, 4294967297
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Also, numbers m such that (4^k)^(m-1) == 1 (mod (m-1)^2 + 1) for all k >= 0.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
5 is a term because 4^(5-1) == 1 (mod (5-1)^2+1), i.e., 255 == 0 (mod 17).
|
|
PROG
|
(Magma) [n: n in [1..100000] | (4^(n-1)-1) mod ((n-1)^2+1) eq 0]
(PARI) isok(n) = Mod(4, (n-1)^2+1)^(n-1) == 1; \\ Michel Marcus, Jun 02 2016
|
|
CROSSREFS
|
Contains A000215 (Fermat numbers) as subsequence.
Contains 1 + A247220 as subsequence.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|