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Search: id:A054272
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| A054272 |
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Number of primes in interval [p(n),p(n)^2]. |
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+0
3
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| 2, 3, 7, 12, 26, 34, 55, 65, 91, 137, 152, 208, 251, 270, 315, 394, 471, 502, 591, 656, 685, 790, 864, 977, 1139, 1227, 1268, 1354, 1395, 1494, 1847, 1945, 2109, 2157, 2455, 2512, 2693, 2878, 3005, 3202, 3396, 3471, 3826, 3902, 4045, 4119, 4581, 5059
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These primes are candidates for fortunate numbers (A005235).
These are precisely the primes available for the solution of Aguilar's conjecture or Haga's conjecture in Carlos Rivera's The Prime Puzzles and Problems Connection, (conjecture 26). Aguilar's conjecture states that at least one prime will be available for placement on each row and column of a p x p square array. Haga's conjecture states that just p primes are required for such placement in any p x p array. - Enoch Haga (Enokh(AT)comcast.net), Jan 23 2002
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REFERENCES
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Carlos Rivera, The Prime Puzzles and Problems Connection (Conjecture 26)
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FORMULA
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a(n)=A000879[n]-n+1
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EXAMPLE
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n=4, the zone in question is [7,49] and encloses a(4)=12 primes, as follows: {7,11,13,17,19,23,29,31,37,41,43,47}
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CROSSREFS
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A000879, A001248, A000040, A005235.
Sequence in context: A108742 A018240 A090596 this_sequence A129016 A099163 A000676
Adjacent sequences: A054269 A054270 A054271 this_sequence A054273 A054274 A054275
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 05 2000
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