A321462 Primes p for which, if q is the greatest prime < p, there exists a prime r < q such that r*q == 1 (mod p).

5, 7, 23, 67, 71, 79, 179, 191, 239, 311, 317, 431, 439, 479, 557, 599, 607, 683, 709, 719, 743, 773, 787, 797, 809, 863, 911, 1031, 1039, 1103, 1171, 1213, 1223, 1381, 1493, 1499, 1583, 1627, 1637, 1663, 1733, 1759, 1777, 1811, 1867, 1973, 1997, 2053, 2099

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

p = 5 is a term, because then q = 3, and 3*2 = 6 == 1 (mod 5).
p = 23 is a term, because then q = 19, and 19*17 = 323 == 1 (mod 23).

Maple

for n from 1 to 300 do
X := ithprime(n);
Y := ithprime(n+1);
Z := 1/X mod Y;
if Z < X and isprime(Z) then print(Y);
end if:
end do:

Mathematica

aQ[p_]:=Module[{p1=NextPrime[p, -1]}, ans=False; p2=2; While[p2<p1, If[Mod[p1*p2, p]==1, ans=True; Break[]]; p2=NextPrime[p2]]; ans]; Select[Prime[Range[317]], aQ] (* Amiram Eldar, Nov 10 2018 *)

Prog

(PARI) is(n) = my(q=precprime(n-1)); forprime(r=1, q-1, if(Mod(r*q, n)==1, return(1))); 0
forprime(p=1, , if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Nov 10 2018
(PARI) upto(n) = {my(q = 3, r, res = List()); forprime(p = 5, n, r = gcdext(q, p)[1]; while(r < 0, r+=p); if(isprime(r), listput(res, p)); q = p); res} \\ David A. Corneth, Nov 10 2018

Crossrefs

Sequence in context: A173970 A028287 A293861 * A121605 A226657 A229021

Adjacent sequences: A321459 A321460 A321461 * A321463 A321464 A321465

Keyword

nonn,easy

Author

David James Sycamore, Nov 10 2018

Extensions

More terms from Felix Fröhlich, Nov 10 2018

Status

approved