|
Search: id:A138508
|
|
|
| A138508 |
|
Semiprime analogue 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 prime is ever reached. |
|
+0
1
|
|
| 4, 6, 3, 1, 5, 1, 2, 3, 1, 1, 4, 2, 3, 1, 1, 2, 2, 5, 2, 5, 1, 1, 3, 2, 1, 1, 2, 2, 3, 3, 5, 2, 1, 1, 1, 4, 4, 1, 1, 4, 4, 2, 2, 8, 2, 1, 2, 4, 1, 3, 1, 11, 3, 3, 1, 7, 1, 1, 2, 2, 2, 1, 4, 2, 1, 2, 4, 4, 1, 2, 2, 2, 3, 1, 3, 6, 1, 5, 2, 2, 3, 1, 3, 2, 1, 1, 1, 2, 7, 6, 1, 2, 1, 1, 1, 6, 3, 3, 4, 2, 2, 2, 3, 2, 10
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
This to A050412 as semiprimes A001358 are to primes A000040.
|
|
FORMULA
|
a(n)=1+(smallest m>=0 such that (n+1)*2^m-1 is semiprime), or 0 if no such semiprime exists. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
|
|
EXAMPLE
|
a(52) = 11 because there are 11 steps in the iteration until a semiprime, namely 52; 2*423+1 = 847 = 7 * 11^2; 2*847+1 = 1695 = 3 * 5 * 113; 2*1695+1 = 3391 (prime); 2*3391+1 = 6783 = 3 * 7 * 17 * 19; 2*6783+1 = 13567 (prime); 2*13567+1 = 27135 = 3^4 * 5 * 67; 2*27135+1 = 54271 = 7 * 7753, which is semiprime.
|
|
MAPLE
|
isA001358 := proc(n) RETURN( numtheory[bigomega](n) = 2) ; end: A138508 := proc(n) local a, niter ; niter := n ; a := 1 ; while not isA001358(niter) do a := a+1 ; niter := 2*niter+1 ; od: a ; end: seq(A138508(n), n=1..200) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
|
|
CROSSREFS
|
Cf. A001358, A050412.
Sequence in context: A087231 A019211 A086467 this_sequence A016492 A081709 A073000
Adjacent sequences: A138505 A138506 A138507 this_sequence A138509 A138510 A138511
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), May 10 2008
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
|
|
|
Search completed in 0.003 seconds
|
