

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
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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 3factor Carmichael numbers.


LINKS

Table of n, a(n) for n=1..27.
OEIS index entries for Carmichael numbers


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, p1, B=ceil((p^2+1)/A); while( 1, r=(p*Bp+A*BB)/(A*Bp*p); q=(A*rA+1)/p; q<=p && break; denominator(q)==1 && denominator(r)==1 && r>q && isprime(q) && isprime(r) && (p*q*r)%(p1)==1 && V=concat(V, [p*q*r]); B++ )); if( V, vecmin( V )); }


CROSSREFS

Cf. A002997, A051663, A135720, A141702A141706.
Sequence in context: A224695 A137198 A194231 * A135721 A047713 A006971
Adjacent sequences: A141702 A141703 A141704 * A141706 A141707 A141708


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jul 03 2008


STATUS

approved



