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%I #7 Mar 31 2012 10:26:04
%S 3,5,113,1193,13883,312311,10861751,209551343,10705778183,
%T 307525001783,10418232047123,795076554810539,17714426958677549,
%U 1015246475642397989,100019969411961789191,1728838135940697098327,165000496158437438012513
%N Smallest prime that becomes a product of n distinct primes when a 1 is prepended to it.
%C We have a(2)=5 because 5 is the smallest prime (ahead of 11,19,19,23,29,...) that is a product of two distinct primes when a 1 is prepended.
%o (PARI) {len10(n) = ceil(log(n+1)/log(10))} {r(n,p,d)=local(q);if(d==0,k=n-10^(len10(n)-1);if(len10(k)==len10(n)-1 && isprime(k),m=n);return);q=nextprime(p+1);while(n*q^d<m,r(n*q,q,d-1);q=nextprime(q+1))} {A105526(d) = M=3^d;while(1,m=M;r(1,2,d);if(m!=M,return(m%10^(len10(m)-1)));M*=2)} (Alekseyev)
%Y Cf. A105525.
%K nonn,base
%O 1,1
%A _Lekraj Beedassy_, Apr 11 2005
%E a(5)-a(8) from _Ray Chandler_, Apr 21 2005
%E More terms from _Max Alekseyev_, Apr 28 2005
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