A051663 - OEIS

A051663

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

2, 11, 197, 1223, 1487, 4007, 4547, 7823, 9833, 9839, 10259, 11483, 11807, 11909, 13259, 13967, 14207, 15629, 15803, 16139, 16889, 18287, 19583, 22367, 23039, 23879, 24359, 25349, 29339, 30707, 32027, 33343, 34883, 36929, 38747

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OFFSET

1,1

REFERENCES

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

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..544 (all terms < 10^6)

Index entries for sequences related to Carmichael numbers

EXAMPLE

2 is a term since there is no Carmichael number of the form 2rq.

PROG

(PARI) is(p) = {

for( A=1, p-1,

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

while(1,

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

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

if(p>=q, break);

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

B++

)

);

}; \\ Charles R Greathouse IV, Feb 23 2013

CROSSREFS

Sequence in context: A140314 A226052 A271429 * A348859 A358649 A188203

Adjacent sequences: A051660 A051661 A051662 * A051664 A051665 A051666

KEYWORD

nonn

AUTHOR

Gilberto Garcia-Pulgarin, Dec 11 1999

EXTENSIONS

Edited by Jack Brennen, Jul 01 2008

Corrected by Emmanuel Vantieghem, Nov 26 2012

STATUS

approved