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Search: id:A030469
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| A030469 |
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Primes which are concatenations of three consecutive primes. |
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3
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| 5711, 111317, 171923, 313741, 414347, 8997101, 229233239, 239241251, 263269271, 307311313, 313317331, 317331337, 353359367, 359367373, 383389397, 389397401, 401409419, 409419421, 439443449, 449457461
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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P(n) = "p(k) p(k+1) p(k+2)" where p(k) is k-th prime
It is conjectured that sequence is infinite. - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
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REFERENCES
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Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Rss¤tsels der Mathematik, Beck, Muenchen 2004 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
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LINKS
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Zak Seidov, Table of n, a(n) for n=1..1000. [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 16 2009]
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FORMULA
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A132903 INTERSECT A000040. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2009]
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EXAMPLE
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(1) 5=p(3), 7=p(4), 11=p(5) give P(1) for k=3 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
(2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
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MATHEMATICA
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Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n], Prime[n+1], Prime[n+2]}]], {n, 11000}], PrimeQ] [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 16 2009]
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PROGRAM
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(PARI) for(i=1, 999, isprime(p=eval(Str(prime(i), prime(i+1), prime(i+2)))) & print1(p, " ")) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 10 2009]
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CROSSREFS
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Cf. A030461 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
Cf. A167517, A132903, A068655, A030997, A030473, A086041, A099727. [From M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 10 2009]
Sequence in context: A022010 A151770 A025027 this_sequence A028547 A043484 A163027
Adjacent sequences: A030466 A030467 A030468 this_sequence A030470 A030471 A030472
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KEYWORD
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nonn,new,base
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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