|
| |
|
|
A182297
|
|
Wieferich numbers (2): positive odd integers q such that q and (2^A002326((q-1)/2)-1)/q are not relatively prime.
|
|
2
|
|
|
|
21, 39, 55, 57, 105, 111, 147, 155, 165, 171, 183, 195, 201, 203, 205, 219, 231, 237, 253, 273, 285, 291, 301, 305, 309, 327, 333, 355, 357, 385, 399, 417, 429, 453, 465, 483, 489, 495, 497, 505, 507, 525, 543, 555, 579, 597, 605, 609, 615, 627, 633, 651, 655
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
Z. Franco and C. Pomerance, On a conjecture of Crandall concerning the qx + 1 problem, Math. Comp. Vol. 64, No. 211 (1995), 1333-1336.
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 1..1000
|
|
|
EXAMPLE
|
21 is in the sequence because the multiplicative order of 2 mod 21 is 6, and (2^6-1)/21 = 3, which is not coprime to 21.
|
|
|
MAPLE
|
with(numtheory):
a:= proc(n) option remember; local q;
for q from 2 +`if`(n=1, 1, a(n-1)) by 2
while igcd((2^order(2, q)-1)/q, q)=1 do od; q
end:
seq (a(n), n=1..60); # Alois P. Heinz, Apr 23 2012
|
|
|
MATHEMATICA
|
Select[Range[1, 799, 2], GCD[#, (2^MultiplicativeOrder[2, #] - 1)/#] > 1 &] (* Alonso del Arte, Apr 23 2012 *)
|
|
|
CROSSREFS
|
For another definition of Wieferich numbers, see A077816.
Cf. A002326.
Sequence in context: A072708 A102478 A221048 * A020220 A084856 A070666
Adjacent sequences: A182294 A182295 A182296 * A182298 A182299 A182300
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Felix Fröhlich, Apr 23 2012
|
|
|
STATUS
|
approved
|
| |
|
|
