|
|
A064164
|
|
EHS numbers: k such that there is a prime p satisfying k! + 1 == 0 (mod p) and p !== 1 (mod k).
|
|
4
|
|
|
8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Hardy & Subbarao prove that this sequence is infinite, see their Theorem 2.12. - Charles R Greathouse IV, Sep 10 2015
|
|
LINKS
|
|
|
MATHEMATICA
|
Do[k = 1; While[p = Prime[k]; k < 10^8 && Not[ Nor[ Mod[n! + 1, p] != 0, Mod[p, n] == 1]], k++ ]; If[k != 10^8, Print[n, " ", p]], {n, 2, 88}]
|
|
PROG
|
(PARI) is(n)=my(f=factor(n!+1)[, 1]); for(i=1, #f, if(f[i]%n != 1, return(n>1))); 0 \\ Charles R Greathouse IV, Sep 10 2015
|
|
CROSSREFS
|
The smallest associated primes p are given in A064229.
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected and extended by Don Reble, Sep 23 2001
|
|
STATUS
|
approved
|
|
|
|