login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238460 Primes p for which x! + (p-1)!/x!==0 (mod p)  has only two solutions 1<=x<=p-2 following from Wilson theorem: x = 1 and x = p-2. 3
5, 13, 37, 41, 101, 113, 157, 173, 181, 197, 229, 241, 281, 313, 337, 349, 353, 373, 409, 421, 433, 509, 541, 617, 677, 701, 757, 761, 769, 773, 821, 929, 941, 977, 997, 1013, 1093, 1097, 1109, 1181, 1193, 1237, 1409, 1433, 1481, 1489, 1669, 1693, 1721, 1741 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is prime(k(n)) for which A238444(k(n)) = 2.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n) == 1 (mod 4).

Proof. Using Wilson's theorem, for every p>3, p==3(mod 4) we have, at least, 3 solution in [1,p-2] of x! + (p-1)!/x!==0 (mod p): x = 1, x = (p-1)/2, x = p-2.

MATHEMATICA

A238444[n_] := a[n] = Module[{p, r}, p = Prime[n]; r = Range[p-2]; Count[r!+(p-1)!/r!, k_ /; Divisible[k, p]]]; A238460 = Prime /@ (Position[Table[A238444[n], {n, 1, 300}], 2] // Flatten) (* Jean-Fran├žois Alcover, Feb 27 2014 *)

PROG

(PARI) is(p)=if(!isprime(p), return(0)); my(X=Mod(1, p), P=Mod((p-1)!, p)); for(x=2, p-3, X*=x; P/=x; if(X+P==0, return(0))); p>3 \\ Charles R Greathouse IV, Feb 28 2014

CROSSREFS

Cf. A238444.

Sequence in context: A266102 A288180 A141408 * A107144 A137815 A089523

Adjacent sequences:  A238457 A238458 A238459 * A238461 A238462 A238463

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Feb 27 2014

EXTENSIONS

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

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 07:11 EST 2019. Contains 329785 sequences. (Running on oeis4.)