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A114787
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Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.
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0
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0, 53, 0, 557, 55511, 55555555555555555555555555555555555555555555555555555555555555555555513, 55555517, 5519, 523, 55529, 5531
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Prime(n) is all zeros followed by prime(n). This is all fives followed by prime(n). Conjecture: No term is zero for n > 3.
The next sequence in this progression, "Smallest prime of the form: all sixes followed by prime(n), a(n)> prime(n)", begins 0, 0, 0, 67, then (5) = 2*(10^5039 - 1)/3 - 55, a number that consists of 5037 sixes followed by 2 ones. This does not fit into the constraints of the OEIS. N. J. A. Sloane (njas(AT)research.att.com), Nov 20 2005, based on information from Hans Havermann.
The large prime here is only a probable prime. The next term, if it exists, is more than 10^1000, followed by 541 55555543 547 55555553 55555559 ... - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 06 2006
The large number *is* prime, quickly certified by APRCL test in PARI: isprime(555...513,2) -> 1 [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 17 2009]
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EXAMPLE
| a(5) = 55511, as 511, 5511 are composite, prime(5) = 11.
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CROSSREFS
| Cf. A114783, A114784, A114785, A114786.
Sequence in context: A198912 A038778 A116107 * A198776 A051320 A078681
Adjacent sequences: A114784 A114785 A114786 * A114788 A114789 A114790
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KEYWORD
| base,more,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 17 2005
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EXTENSIONS
| More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 06 2006
Edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2008
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