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Search: id:A066352
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| A066352 |
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Marcos sequence: a(n) is the smallest term A007924(i) requiring n primes. |
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+0 2
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OFFSET
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0,3
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COMMENT
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Conjecture: To locate the next number, we need to spot consecutive 1354 composite numbers, that is a prime gap (=difference of consecutive primes) of at least 1355. This starts at the prime 401429925999153707 (<a href="http://www.trnicely.net/gaps/gaplist.html">T R Nicely's gap list</a>) and this generates a(5)=4014...707+1354=401429925999155061. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 27 2007
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REFERENCES
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a(4) computed by Carlos Rivera, solutions of puzzle 141 by Chris Nash, Jud McCranie, Key Toshihara, Chu Lai, Felice Russo, and Motua Guang.
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LINKS
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M. T. Marcos, Smarandache Prime Base representation, prime puzzle 141.
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FORMULA
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a(n) = 2*p(m) - p(m-1) with minimal m = pi(a(n)) so that p(m) = a(n-1) + p(m-1).
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EXAMPLE
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a(3) = 23+3+1 = p(9)+p(2)+p(0) is the first n with 3 ones in 1000000101 = A007924(27).
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CROSSREFS
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p(n) = A008578(n), A007924 (binary Smarandache Prime Base representation).
Adjacent sequences: A066349 A066350 A066351 this_sequence A066353 A066354 A066355
Sequence in context: A066842 A133032 A110763 this_sequence A051674 A132641 A008973
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KEYWORD
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more,nonn
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AUTHOR
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Copied from www.primepuzzles.net by frank.ellermann(AT)t-online.de, Dec 19 2001.
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EXTENSIONS
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The next term is > 4.29E17. It occurs where there is a gap of at least 1354 between two consecutive primes. - Randall L. Rathbun (randallr(AT)abac.com), Jan 27 2002
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