OFFSET
1,1
COMMENTS
Conjecture: only Carmichael numbers of the form 10n+1 can have prime divisors of the form 10k+1 (but not all Carmichael numbers of the form 10n+1 have prime divisors of the form 10k+1).
Checked up to Carmichael number 4954039956700380001.
Conjecture: all Carmichael numbers C (not only with three prime divisors) of the form 10n+1 that have only prime divisors of the form 10k+1 can be written as C = (30a+1)*(30b+1)*(30c+1), C = (30a+11)*(30b+11)*(30c+11), or C = (30a+1)*(30b+11)*(30c+11). In other words, there are no numbers of the form C = (30a+1)*(30b+1)*(30c+11).
Checked for all Carmichael numbers from the sequence above.
The first conjecture is a consequence of Korselt's criterion. - Charles R Greathouse IV, Oct 02 2012
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
E. W. Weisstein, Carmichael Number
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius Coman, May 28 2012
EXTENSIONS
Terms corrected by Charles R Greathouse IV, Oct 02 2012
STATUS
approved