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Semiprimes p*q such that the concatenation p||q is again a semiprime, where p <= q.
2

%I #6 Mar 31 2012 13:48:31

%S 4,9,10,15,25,26,34,35,38,49,55,57,69,74,85,87,91,94,95,106,118,119,

%T 121,123,134,145,161,169,178,183,185,202,206,209,213,215,217,221,254,

%U 259,265,289,295,298,303,309,314,321,334,339,346,361,362,365,371,377,381,382,393,395,398,407,415,417,437,445,447,451,453,454,458

%N Semiprimes p*q such that the concatenation p||q is again a semiprime, where p <= q.

%e a(1)=4 because 4=2*2 and 22=2*11 are semiprimes.

%e The semiprime 6=2*3 is not in the sequence, because the concatenation 2||3 = 23 is not a semiprime.

%e a(2)=9 because 9=3*3 and 33=3*11 are semiprimes.

%e a(3)=10 because 10=2*5 and 25=5*5 are semiprimes.

%e The semiprime 14=2*7 is not in the sequence, because 2||7 = 27 = 3*3*3 is not a semiprime.

%e a(4)=15 because 15=3*5 and 35=5*7 are semiprimes.

%o (PARI) for(i=1,500,bigomega(i)==2|next;f=factor(i)~;bigomega(eval(Str(f[1,1],f[1,#f])))==2&print1(i","))

%Y Cf. A001358.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jun 19 2011