A123386 Largest difference between successive semiprimes up to 10^n inclusive.

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

Offset: 1

Author

Alexander Adamchuk, Nov 09 2006

Keywords

• hard
• more
• nonn

Comments

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.

Crossrefs

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

Programs

PARI

A001358(prev)={ local(a=prev+1) ; while(bigomega(a)!=2, a++ ; ) ; return(a) ; }
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) ; }
{ for(n=1,13, print(A123386(n)) ; ) ; } \\ 2 more terms from R. J. Mathar, Jan 17 2008

Extensions

2 more term from R. J. Mathar, Jan 17 2008

a(8)-a(9) from Donovan Johnson, Sep 05 2008

a(10)-a(11) from Donovan Johnson, Apr 14 2010

a(12)-a(13) from Donovan Johnson, Sep 20 2012