A123386 - OEIS

%I #14 Nov 23 2024 14:35:41

%S 3,7,14,24,38,47,74,74,95,112,146,163,174

%N Largest difference between successive semiprimes up to 10^n inclusive.

%C There are 4 semiprimes up to 10^1 {4, 6, 9, 10}. The differences between successive semiprimes are {2, 3, 1}. Thus a(1) = Max[ {2, 3, 1} ] = 3.

%o (PARI)

%o A001358(prev)={ local(a=prev+1) ; while(bigomega(a)!=2, a++ ; ) ; return(a) ; }

%o A123386(n)={ local(sp1=4,sp2=6,a=2) ; while(sp2<=10^n, a=max(a,sp2-sp1) ; sp1=sp2 ; sp2=A001358(sp1) ; ) ; return(a) ; }

%o { for(n=1,13, print(A123386(n)) ; ) ; } \\ 2 more terms from _R. J. Mathar_, Jan 17 2008

%Y Cf. A001358, A065516, A036352, A038460, A053303.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 09 2006

%E 2 more term from _R. J. Mathar_, Jan 17 2008

%E a(8)-a(9) from _Donovan Johnson_, Sep 05 2008

%E a(10)-a(11) from _Donovan Johnson_, Apr 14 2010

%E a(12)-a(13) from _Donovan Johnson_, Sep 20 2012