

A064164


EHS numbers: n such that there is a prime p satisfying n!+1 = 0 mod p and p not equal to 1 mod n.


3



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
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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

Table of n, a(n) for n=1..67.
G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109:6 (2002), pp. 554559.
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.
Cf. A002981, A064295.
Sequence in context: A167131 A109079 A050883 * A079525 A083131 A101591
Adjacent sequences: A064161 A064162 A064163 * A064165 A064166 A064167


KEYWORD

nonn,nice


AUTHOR

R. K. Guy, Sep 20 2001


EXTENSIONS

Corrected and extended by Don Reble, Sep 23 2001


STATUS

approved



