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A138508
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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.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This to A050412 as semiprimes A001358 are to primes A000040.
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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
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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.
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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
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CROSSREFS
| Cf. A001358, A050412.
Sequence in context: A204174 A086467 A197731 * A016492 A200365 A198121
Adjacent sequences: A138505 A138506 A138507 * A138509 A138510 A138511
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 10 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
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