|
|
A187849
|
|
Integers k such that 2^(k-1) == 1 (mod k) and 2^(m-1) == 1 (mod m), where m is defined as m = k*(A000265(k-1) - 1) + 1.
|
|
1
|
|
|
563, 1291, 1733, 1907, 2477, 2609, 2693, 2837, 3533, 3677, 4157, 4517, 5693, 12809, 15077, 19997, 25603, 28517, 29573, 29837, 31517, 32237, 32717, 34949, 37277, 43613, 43973, 44453, 50333, 52253, 62477, 68213, 69197, 72893, 74717
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The first condition of the definition means terms k are either primes or Fermat pseudoprimes to base 2 (see A001567). If the parameter m is also prime or Fermat pseudoprime to base 2, then k belongs to this sequence.
Composites in this sequence: 1771946607940820033, 14356915031659973281, ... - Max Alekseyev
If k = 1 and p is a composite number, then p == 0 (mod 3). (Is this heuristics or strict? - R. J. Mathar, Apr 04 2011) Terms to illustrate these cases:
k = 1291 = 2 * 645 + 1; p = 645 = 215 * 3.
k = 25603 = 2 * 12801 + 1; p = 12801 = 4267 * 3.
k = 424843 = 2 * 212421 + 1; p = 212421 = 70807 * 3.
k = 579883 = 2 * 289941 + 1; p = 289941 = 96647 * 3.
k = 4325443 = 2 * 2162721 + 1; p = 2162721 = 720907 * 3.
|
|
LINKS
|
|
|
MAPLE
|
isA187849 := proc(n) local redn, k, p, m; if modp(2^(n-1), n) = 1 then redn := n-1 ; k := A007814(redn) ; p := (n-1)/2^k ; m := n*(p-1)+1 ; is( modp(2^(m-1), m) = 1 ); else false; end if; end proc:
for n from 1 do if isA187849(n) then print(n); end if; end do: # R. J. Mathar, Mar 30 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|