cp's OEIS Frontend

A051663 Primes p such that there is no Carmichael number pqr, p q, r primes.

%I A051663 #26 May 12 2024 10:03:24
%S A051663 2,11,197,1223,1487,4007,4547,7823,9833,9839,10259,11483,11807,11909,
%T A051663 13259,13967,14207,15629,15803,16139,16889,18287,19583,22367,23039,
%U A051663 23879,24359,25349,29339,30707,32027,33343,34883,36929,38747
%N A051663 Primes p such that there is no Carmichael number pqr, p<q<r q, r primes.
%D A051663 Gilberto Garcia-Pulgarin, Numeros de Carmichael producto de tes primos, preprint, 1999.
%H A051663 Charles R Greathouse IV, <a href="/A051663/b051663.txt">Table of n, a(n) for n = 1..544</a> (all terms < 10^6)
%H A051663 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>
%e A051663 2 is a term since there is no Carmichael number of the form 2rq.
%o A051663 (PARI) is(p) = {
%o A051663     for( A=1, p-1,
%o A051663         my(B=ceil((p^2+1)/A),q,r);
%o A051663         while(1,
%o A051663             r=(B*(p+A-1)-p)/(A*B-p*p);
%o A051663             q=(A*r-A+1)/p;
%o A051663             if(p>=q, break);
%o A051663             if(denominator(q)==1 && denominator(r)==1 && r>q && (q*r)%(p-1)==1 && isprime(q) && isprime(r), return(0));
%o A051663             B++
%o A051663         )
%o A051663     );
%o A051663     1
%o A051663 }; \\ _Charles R Greathouse IV_, Feb 23 2013
%K A051663 nonn
%O A051663 1,1
%A A051663 _Gilberto Garcia-Pulgarin_, Dec 11 1999
%E A051663 Edited by Jack Brennen, Jul 01 2008
%E A051663 Corrected by _Emmanuel Vantieghem_, Nov 26 2012