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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).
1
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Felix Fröhlich, Nov 10 2018
STATUS
approved