

A238501


Primes p for which x! + (p1)!/x!==0 (mod p) has only three solutions 1<=x<=p2.


0



7, 11, 19, 31, 43, 47, 107, 127, 131, 151, 163, 167, 179, 191, 211, 223, 263, 283, 347, 367, 443, 487, 491, 523, 547, 587, 643, 659, 751, 827, 839, 911, 1039, 1051, 1087, 1103, 1123, 1163, 1171, 1223, 1259, 1283, 1291, 1327, 1427, 1439, 1447, 1487, 1523, 1543
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OFFSET

1,1


COMMENTS

All terms are of the form 4*k+3.
Using Wilson's theorem, for every p>3, p==3(mod 4) we have, at least, 3 solutions in [1,p2] of x! + (p1)!/x!==0 (mod p): x = 1, x = (p1)/2, x = p2.


LINKS

Table of n, a(n) for n=1..50.


FORMULA

a(n) is prime(k(n)) for which A238444(k(n)) = 3.


MATHEMATICA

kmax = 400; Select[Select[4*Range[kmax]+3, PrimeQ], (r = Range[#2]; Count[r!+(#1)!/r!, k_ /; Divisible[k, #]] == 3)&] (* JeanFrançois Alcover, Mar 05 2014 *)


CROSSREFS

Cf. A238444, A238460.
Sequence in context: A053403 A032672 A235806 * A133425 A103802 A038984
Adjacent sequences: A238498 A238499 A238500 * A238502 A238503 A238504


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Feb 27 2014


EXTENSIONS

More terms from Peter J. C. Moses, Feb 27 2014


STATUS

approved



