

A114787


Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.


0



0, 53, 0, 557, 55511, 55555555555555555555555555555555555555555555555555555555555555555555513, 55555517, 5519, 523, 55529, 5531, 0, 541, 55555543, 547, 55555553, 55555559
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OFFSET

1,2


COMMENTS

Prime(n) is all zeros followed by prime(n). This is all fives followed by prime(n).
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, Nov 20 2005, based on information from Hans Havermann.
The large number is quickly certified prime by PARI's APRCL test: isprime(555...513,2) > 1.  Hagen von Eitzen, Jun 17 2009
Next term is 5*(10^184  1)/9 + 6, containing 184 digits, and is too large to include here.  Arkadiusz Wesolowski, Jun 03 2013


LINKS

Table of n, a(n) for n=1..17.


EXAMPLE

a(5) = 55511, as 511, 5511 are composite, prime(5) = 11.
All positive numbers of the form 5*(10^k  1)/9  18 have a factor in the covering set {3, 7, 13, 37}, so a(12) = 0.  Arkadiusz Wesolowski, Jun 03 2013


CROSSREFS

Cf. A114783, A114784, A114785, A114786.
Sequence in context: A208300 A038778 A116107 * A198776 A051320 A232126
Adjacent sequences: A114784 A114785 A114786 * A114788 A114789 A114790


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Nov 17 2005


EXTENSIONS

More terms from Joshua Zucker, May 06 2006
Edited by T. D. Noe, Oct 30 2008
a(12)a(17) from Arkadiusz Wesolowski, Jun 03 2013


STATUS

approved



