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 A141705 a(n) = least Carmichael number of the form prime(n)*prime(n')*prime(n") with n < n' < n", or 0 if no such number exists. 2
 0, 561, 1105, 1729, 0, 29341, 162401, 334153, 1615681, 3581761, 399001, 294409, 252601, 1152271, 104569501, 2508013, 178837201, 6189121, 10267951, 10024561, 14469841, 4461725581, 985052881, 19384289, 23382529, 3828001, 90698401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Primes for which there are no such numbers (i.e. prime(n) such that a(n)=0) are given in A051663. Sequence A135720 is similar, but without restriction to 3-factor Carmichael numbers. LINKS EXAMPLE a(1)=0 since there is no Carmichael number having prime(1)=2 as factor. a(2)=561 since this is the smallest Carmichael number of the form pqr with prime r>q>p=prime(2)=3. a(5)=0 since there is no Carmichael number of the form pqr with prime r>q>p=prime(5)=11. PROG (PARI) A141705(n) = { /* based on code by J.Brennen (jb AT brennen.net) */ local( V=[], B, p=prime(n), q, r); for( A=1, p-1, B=ceil((p^2+1)/A); while( 1, r=(p*B-p+A*B-B)/(A*B-p*p); q=(A*r-A+1)/p; q<=p && break; denominator(q)==1 && denominator(r)==1 && r>q && isprime(q) && isprime(r) && (p*q*r)%(p-1)==1 && V=concat(V, [p*q*r]); B++ )); if( V, vecmin( V )); } CROSSREFS Cf. A002997, A051663, A135720, A141702-A141706. Sequence in context: A224695 A137198 A194231 * A135721 A253595 A047713 Adjacent sequences:  A141702 A141703 A141704 * A141706 A141707 A141708 KEYWORD nonn AUTHOR M. F. Hasler, Jul 03 2008 STATUS approved

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