login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
The complement of this sequence (A064295) is a superset of A002981.
Hardy & Subbarao prove that this sequence is infinite, see their Theorem 2.12. - Charles R Greathouse IV, Sep 10 2015
LINKS
G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109:6 (2002), pp. 554-559.
H. Mishima, Factors of N!+1
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.
Sequence in context: A167131 A109079 A050883 * A079525 A083131 A101591
KEYWORD
nonn,nice
AUTHOR
R. K. Guy, Sep 20 2001
EXTENSIONS
Corrected and extended by Don Reble, Sep 23 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)