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Search: id:A036440
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| A036440 |
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Number of ways of arranging row n of the Prime Pyramid. |
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+0
7
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| 1, 1, 1, 1, 1, 1, 2, 4, 7, 24, 80, 216, 648, 1304, 3392, 13808, 59448, 155464, 480728, 1588162, 5626309, 28279112, 157469880, 842498189, 4998554801, 28466978744, 166572523589
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Number of ways to arrange numbers from 1 to n in a row, starting with 1 and ending with n, such that the sum of every two adjacent numbers is prime.
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, C1.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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a(8)=4 because of the 720 permutations P of {1,2,3,...,8) with first element 1 and last element 8, these four satisfy the "prime pyramid" condition that P[ i ]+P[ i+1 ] be prime for i=1..7: 1 2 3 4 7 6 5 8; 1 2 5 6 7 4 3 8; 1 4 7 6 5 2 3 8; 1 6 7 4 3 2 5 8.
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CROSSREFS
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Cf. A051237.
Sequence in context: A059501 A138049 A099387 this_sequence A103001 A065846 A047904
Adjacent sequences: A036437 A036438 A036439 this_sequence A036441 A036442 A036443
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KEYWORD
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nonn,nice
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net)
a(25..27) from Max Alekseyev (maxale(AT)gmail.com), Jan 05 2008
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