A064164 EHS numbers: k such that there is a prime p satisfying k! + 1 == 0 (mod p) and p !== 1 (mod k).

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

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

Amiram Eldar, Table of n, a(n) for n = 1..120

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.

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