A138508 Semiprime analog of Riesel problem: start with n; repeatedly double and add 1 until reach a semiprime. Sequence gives number of steps to reach a semiprime or 0 if no semiprime is ever reached.

3, 5, 2, 1, 4, 3, 1, 2, 2, 1, 3, 1, 2, 3, 5, 1, 1, 4, 1, 4, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2, 4, 1, 4, 1, 2, 3, 3, 1, 2, 3, 3, 1, 1, 7, 1, 1, 1, 3, 4, 2, 3, 10, 2, 2, 1, 6, 1, 2, 1, 1, 1, 4, 3, 1, 3, 1, 3, 3, 3, 1, 1, 1, 2, 2, 2, 5, 1, 4, 1, 1, 2, 6, 2, 1, 3, 3, 3, 1, 6, 5, 1, 1, 1, 5, 3, 5, 2, 2, 3, 1, 1, 1, 2, 1, 9, 1, 1, 1, 1, 1, 2

Offset: 1

Author

Jonathan Vos Post, May 10 2008

Keywords

• easy
• nonn

Comments

This is the analog of A050412 with "prime" replaced by "semiprime". [Edited by Felix Fröhlich, Apr 21 2021]

a(n) is the smallest m>=0 such that (n+1)*2^m-1 is semiprime, or 0 if no such semiprime exists. - R. J. Mathar, May 12 2008

There is no "semiprime Riesel number" (i.e., n such that a(n) = 0) among all n up to 2*10^6. - Felix Fröhlich, Apr 21 2021

Crossrefs

Cf. A001358, A050412.

Programs

Maple

isA001358 := proc(n) RETURN( numtheory[bigomega](n) = 2) ; end:
A138508 := proc(n) local a,niter ; niter := n ; a := 0 ; while not isA001358(niter) do a := a+1 ; niter := 2*niter+1 ; od: a ; end:
seq(A138508(n),n=1..200) ; # R. J. Mathar, May 12 2008

PARI

a(n) = my(x=n, i=0); while(1, x=2*x+1; i++; if(bigomega(x)==2, return(i))); \\ Felix Fröhlich, Apr 21 2021

Extensions

More terms from R. J. Mathar, May 12 2008

All terms corrected by Felix Fröhlich, Apr 21 2021