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Search: id:A008407
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| A008407 |
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Minimal difference s(n) between beginning and end of n consecutive large primes (n-tuplet) permitted by divisibility considerations. |
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+0
9
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| 2, 6, 8, 12, 16, 20, 26, 30, 32, 36, 42, 48, 50, 56, 60, 66, 70, 76, 80, 84, 90, 94, 100, 110, 114, 120, 126, 130, 136, 140, 146, 152, 156, 158, 162, 168, 176, 182, 186, 188, 196, 200, 210, 212, 216, 226, 236, 240, 246, 252, 254, 264, 270, 272, 278
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Tony Forbes defines a prime k-tuplet (distinguished from a prime k-tuple) to be a maximally possible dense cluster of primes (a prime constellation) which will necessarily involve consecutive primes whereas a prime k-tuple is a prime cluster which may not necessarily be of maximum possible density (in which case the primes are not necessarily consecutive.)
a(1) would be 0 (for a prime 1-tuplet.)
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REFERENCES
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R. K. Guy, "Unsolved Problems in Number Theory", lists a number of relevant papers in Section A8.
G. H. Hardy and J.E. Littlewood, "Partitio Numerorum III", Acta Math. 44 (1922) 1-70, see final section.
John Leech, "Groups of primes having maximum density", Math. Tables Aids to Comput., 12 (1958) 144-145.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..672 (from Engelsma's data)
Thomas J. Engelsma, Permissible Patterns
Tony Forbes, k-tuplets
Eric Weisstein's World of Mathematics, Prime Constellation.
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FORMULA
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s(k), k >= 2, is smallest s such that there exist B = {b_1, b_2, ..., b_k} with s = b_k - b_1 and such that for all primes p <= k, not all residues modulo p are represented by B.
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CROSSREFS
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Equals A020497 - 1.
Adjacent sequences: A008404 A008405 A008406 this_sequence A008408 A008409 A008410
Sequence in context: A084724 A111051 A077561 this_sequence A111224 A139718 A135311
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KEYWORD
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nonn,nice
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AUTHOR
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T. Forbes (anthony.d.forbes(AT)googlemail.com)
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EXTENSIONS
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Correction from weidhaas(AT)wotan.llnl.gov (Pat Weidhaas) Jun 15 1997.
Edited by Daniel Forgues (squid(AT)zensearch.com), Aug 13 2009
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