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Search: id:A038664
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| A038664 |
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a(n)-th and (a(n)+1)-st primes are the first pair that differ by 2n. |
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+0
8
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| 2, 4, 9, 24, 34, 46, 30, 282, 99, 154, 189, 263, 367, 429, 590, 738, 217, 1183, 3302, 2191, 1879, 1831, 7970, 3077, 3427, 2225, 3793, 8028, 4612, 4522, 3644, 8688, 14862, 12542, 15783, 3385, 34202, 19026, 17006, 44773, 23283, 38590, 14357
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Does anyone know of a proof that a(n) is defined for all natural numbers n, i.e. f:n -> prime(n+1)-prime(n) is a surjective map from N-{1} -> E, where N, E are the sets of natural numbers and even numbers, respectively? - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 14 2002
a(n) is defined for all n if (but not only if) de Polignac's conjecture is true. - Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 22 2003
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. de Polignac's Conjecture.
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MATHEMATICA
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Table[k = 0; While[k++; p1 = Prime[k]; p2 = Prime[k + 1]; (p2 - p1) != n]; k, {n, 2, 200, 2}] - from Lei Zhou (lzhou5(AT)emory.edu), Mar 01 2005
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CROSSREFS
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Sequence in context: A144309 A080376 A005669 this_sequence A148077 A148078 A093156
Adjacent sequences: A038661 A038662 A038663 this_sequence A038665 A038666 A038667
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KEYWORD
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nonn
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AUTHOR
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Jeff Burch (gburch(AT)erols.com)
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 13 2001
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