cp's OEIS Frontend

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.

%I A141705 #13 Sep 25 2019 10:29:32
%S A141705 0,561,1105,1729,0,29341,162401,334153,1615681,3581761,399001,294409,
%T A141705 252601,1152271,104569501,2508013,178837201,6189121,10267951,10024561,
%U A141705 14469841,4461725581,985052881,19384289,23382529,3828001,90698401
%N 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.
%C A141705 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.
%H A141705 Amiram Eldar, <a href="/A141705/b141705.txt">Table of n, a(n) for n = 1..10000</a>
%H A141705 <a href="/index/Ca#Carmichael">OEIS index entries for Carmichael numbers</a>
%e A141705 a(1)=0 since there is no Carmichael number having prime(1)=2 as factor.
%e A141705 a(2)=561 since this is the smallest Carmichael number of the form pqr with prime r>q>p=prime(2)=3.
%e A141705 a(5)=0 since there is no Carmichael number of the form pqr with prime r>q>p=prime(5)=11.
%o A141705 (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 )); }
%Y A141705 Cf. A002997, A051663, A135720, A141702-A141706.
%K A141705 nonn
%O A141705 1,2
%A A141705 _M. F. Hasler_, Jul 03 2008