A141705 a(n) is the least Carmichael number of the form prime(n)*prime(n')*prime(n") with n < n' < n", or 0 if no such number exists.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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, 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 A290486 A253595

Adjacent sequences: A141702 A141703 A141704 * A141706 A141707 A141708

Keyword

nonn

Author

M. F. Hasler, Jul 03 2008

Status

approved