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Numbers n such that difference between prime factors of n-th semiprime is n.
3

%I #17 Dec 21 2015 12:53:10

%S 5,80,86,613668,6384425704

%N Numbers n such that difference between prime factors of n-th semiprime is n.

%C The 6384425704th semiprime is 44690979977 = 7*6384425711. 6384425711 - 7 = 6384425704. - _Donovan Johnson_, Jul 11 2010

%e sp(5) = 14 = 2*7 and 7 - 2 = 5, sp(80) = 249 = 3*83 and 83 - 3 = 80, sp(86) = 267 = 3*89 and 89 - 3 = 86; sp(n) = n-th semiprime.

%o (PARI)

%o { n=0; j=1; /* n=3068365-1; j=613668;*/

%o while( l=(j\10^4+1)*10^4, until( l < j++, until(bigomega(n+=1)==2,);

%o if(2!=#f=factor(n)[,1],next); if(j==f[2]-f[1],print("\n",[j,n,f])));

%o print1(j-1,":"n", "))} \\ _M. F. Hasler_, Sep 28 2007

%Y Cf. A064910, A084126, A084127, A109313.

%K more,nonn

%O 1,1

%A _Zak Seidov_, Sep 25 2007

%E a(4) = 613668 (p=5, q=613673) from _M. F. Hasler_, Sep 28 2007

%E a(5) from _Donovan Johnson_, Jul 11 2010