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A051663 Primes p such that there is no Carmichael number pqr, p<q<r q, r primes. 5


%S 2,11,197,1223,1487,4007,4547,7823,9833,9839,10259,11483,11807,11909,

%T 13259,13967,14207,15629,15803,16139,16889,18287,19583,22367,23039,

%U 23879,24359,25349,29339,30707,32027,33343,34883,36929,38747

%N Primes p such that there is no Carmichael number pqr, p<q<r q, r primes.

%D Gilberto Garcia-Pulgarin, Numeros de Carmichael producto de tes primos, preprint, 1999.

%H Charles R Greathouse IV, <a href="/A051663/b051663.txt">Table of n, a(n) for n = 1..544</a> (all terms < 10^6)

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>

%e 2 is in the sequence since is no Carmichael number of the form 2rq.

%o (PARI) is(p) = {

%o for( A=1, p-1,

%o my(B=ceil((p^2+1)/A),q,r);

%o while(1,

%o r=(B*(p+A-1)-p)/(A*B-p*p);

%o q=(A*r-A+1)/p;

%o if(p>=q, break);

%o if(denominator(q)==1 && denominator(r)==1 && r>q && (q*r)%(p-1)==1 && isprime(q) && isprime(r), return(0));

%o B++

%o )

%o );

%o 1

%o }; \\ _Charles R Greathouse IV_, Feb 23 2013

%K nonn

%O 1,1

%A _Gilberto Garcia-Pulgarin_, Dec 11 1999

%E Edited by Jack Brennen, Jul 01 2008

%E Corrected by _Emmanuel Vantieghem_, Nov 26 2012

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Last modified April 19 17:46 EDT 2021. Contains 343117 sequences. (Running on oeis4.)