A131867 a(n) is the 2^n-th semiprime.

4, 6, 10, 22, 46, 93, 202, 407, 849, 1774, 3693, 7671, 15999, 33146, 68703, 142682, 295003, 610757, 1261573, 2603453, 5369633, 11058907, 22758881, 46796443, 96132103, 197329777, 404737537, 829538129, 1698995201, 3477431507, 7113030933, 14540737711

Offset: 0

Author

M. F. Hasler, Oct 04 2007

Keywords

• nonn

Comments

The PARI code allows one to resume at the k-th semiprime, e.g., SP(295003,65536) and to change the output interval, e.g., SP(,,10) = A114125, SP(,,-1) = A001358.

Examples

			a(0)=4 is the first semiprime;
a(1)=6 is the 2nd semiprime;
a(16)=295003 is the 65536th semiprime.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 0..59 (first 45 terms from Robert G. Wilson v)

Crossrefs

Cf. A001358 (semiprimes), A114125.

Programs

PARI

SP( n=0 /*tested number*/,c=0 /*count of semiprimes*/, step=2)={ local( l=c+!c ); /* negative/positive step means arithmetic/geometric progression of output threshold l */ until( 0, until(l<=c++,until(bigomega(n+=1)==2,));print1(/*c ":" */ n ", "); if(step>0,l*=step,l-=step))}

Perl

use ntheory ":all"; my($i,$g)=(0,0); forsemiprimes { print $g++," $\n" if ++$i == 1<<$g; } 10**8; # _Dana Jacobsen, Sep 10 2018

Perl

use ntheory ":all"; print "$ ",nth_semiprime(1<<$),"\n" for 0..40; # Dana Jacobsen, Oct 08 2018

Formula

a(n) = A001358(2^n).

Extensions

a(23)-a(28) from Donovan Johnson, Nov 11 2008

a(29)-a(33) from Max Alekseyev, May 07 2010