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- Sylvesters_sequence abstract "In number theory, Sylvester's sequence is an integer sequence in which each member of the sequence is the product of the previous members, plus one. The first few terms of the sequence are:2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence A000058 in OEIS).Sylvester's sequence is named after James Joseph Sylvester, who first investigated it in 1880. Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions with the same number of terms. The recurrence by which it is defined allows the numbers in the sequence to be factored more easily than other numbers of the same magnitude, but, due to the rapid growth of the sequence, complete prime factorizations are known only for a few of its members. Values derived from this sequence have also been used to construct finite Egyptian fraction representations of 1, Sasakian Einstein manifolds, and hard instances for online algorithms.".
- Sylvesters_sequence thumbnail Sylvester-square.svg?width=300.
- Sylvesters_sequence wikiPageExternalLink books?id=1AP2CEGxTkgC&pg=PA346.
- Sylvesters_sequence wikiPageExternalLink caen.pdf.
- Sylvesters_sequence wikiPageExternalLink 1102689567.
- Sylvesters_sequence wikiPageExternalLink DESW_dcfs.ps.
- Sylvesters_sequence wikiPageExternalLink kmath455.htm.
- Sylvesters_sequence wikiPageID "4535485".
- Sylvesters_sequence wikiPageLength "20477".
- Sylvesters_sequence wikiPageOutDegree "63".
- Sylvesters_sequence wikiPageRevisionID "681742470".
- Sylvesters_sequence wikiPageWikiLink 181_(number).
- Sylvesters_sequence wikiPageWikiLink 73_(number).
- Sylvesters_sequence wikiPageWikiLink Acta_Arithmetica.
- Sylvesters_sequence wikiPageWikiLink Algorithm.
- Sylvesters_sequence wikiPageWikiLink American_Journal_of_Mathematics.
- Sylvesters_sequence wikiPageWikiLink American_Mathematical_Monthly.
- Sylvesters_sequence wikiPageWikiLink Annals_of_Mathematics.
- Sylvesters_sequence wikiPageWikiLink Bin_packing.
- Sylvesters_sequence wikiPageWikiLink Bin_packing_problem.
- Sylvesters_sequence wikiPageWikiLink Cahens_constant.
- Sylvesters_sequence wikiPageWikiLink Category:Egyptian_fractions.
- Sylvesters_sequence wikiPageWikiLink Category:Integer_sequences.
- Sylvesters_sequence wikiPageWikiLink Category:Mathematical_series.
- Sylvesters_sequence wikiPageWikiLink Category:Number_theory.
- Sylvesters_sequence wikiPageWikiLink Category:Recurrence_relations.
- Sylvesters_sequence wikiPageWikiLink Composite_number.
- Sylvesters_sequence wikiPageWikiLink Composite_numbers.
- Sylvesters_sequence wikiPageWikiLink Coprime_integers.
- Sylvesters_sequence wikiPageWikiLink Differential_topology.
- Sylvesters_sequence wikiPageWikiLink Double_exponential_function.
- Sylvesters_sequence wikiPageWikiLink Egyptian_fraction.
- Sylvesters_sequence wikiPageWikiLink Einstein_manifold.
- Sylvesters_sequence wikiPageWikiLink Empty_product.
- Sylvesters_sequence wikiPageWikiLink Erdős_conjecture.
- Sylvesters_sequence wikiPageWikiLink Exotic_sphere.
- Sylvesters_sequence wikiPageWikiLink Fermat_number.
- Sylvesters_sequence wikiPageWikiLink Greedy_algorithm_for_Egyptian_fractions.
- Sylvesters_sequence wikiPageWikiLink Group_(mathematics).
- Sylvesters_sequence wikiPageWikiLink Hypersphere.
- Sylvesters_sequence wikiPageWikiLink Integer_factorization.
- Sylvesters_sequence wikiPageWikiLink Integer_sequence.
- Sylvesters_sequence wikiPageWikiLink Irrationality_sequence.
- Sylvesters_sequence wikiPageWikiLink James_Joseph_Sylvester.
- Sylvesters_sequence wikiPageWikiLink List_of_conjectures_by_Paul_Erdős.
- Sylvesters_sequence wikiPageWikiLink Lower_bound.
- Sylvesters_sequence wikiPageWikiLink Multiplicative_inverse.
- Sylvesters_sequence wikiPageWikiLink Nondeterministic_finite_automata.
- Sylvesters_sequence wikiPageWikiLink Nondeterministic_finite_automaton.
- Sylvesters_sequence wikiPageWikiLink Number_theory.
- Sylvesters_sequence wikiPageWikiLink Odd_greedy_expansion.
- Sylvesters_sequence wikiPageWikiLink Online_algorithm.
- Sylvesters_sequence wikiPageWikiLink Pacific_Journal_of_Mathematics.
- Sylvesters_sequence wikiPageWikiLink Perfect_number.
- Sylvesters_sequence wikiPageWikiLink Primary_pseudoperfect_number.
- Sylvesters_sequence wikiPageWikiLink Prime_number.
- Sylvesters_sequence wikiPageWikiLink Reciprocal_(mathematics).
- Sylvesters_sequence wikiPageWikiLink Recurrence_relation.
- Sylvesters_sequence wikiPageWikiLink Relatively_prime.
- Sylvesters_sequence wikiPageWikiLink Riemannian_manifold.
- Sylvesters_sequence wikiPageWikiLink Riemannian_metric.
- Sylvesters_sequence wikiPageWikiLink Sasakian_manifold.
- Sylvesters_sequence wikiPageWikiLink Series_(mathematics).
- Sylvesters_sequence wikiPageWikiLink Sphere.
- Sylvesters_sequence wikiPageWikiLink Springer-Verlag.
- Sylvesters_sequence wikiPageWikiLink Springer_Science+Business_Media.
- Sylvesters_sequence wikiPageWikiLink Square-free_integer.
- Sylvesters_sequence wikiPageWikiLink Telescoping_series.
- Sylvesters_sequence wikiPageWikiLink Topological_sphere.
- Sylvesters_sequence wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
- Sylvesters_sequence wikiPageWikiLink Unit_fraction.
- Sylvesters_sequence wikiPageWikiLink Upper_and_lower_bounds.
- Sylvesters_sequence wikiPageWikiLink Znxc3xa1ms_problem.
- Sylvesters_sequence wikiPageWikiLink File:Sylvester-square.svg.
- Sylvesters_sequence wikiPageWikiLinkText "Sylvester's sequence".
- Sylvesters_sequence wikiPageWikiLinkText "quickly growing integer sequences with rational reciprocal series".
- Sylvesters_sequence authorlink "David Raymond Curtiss".
- Sylvesters_sequence first "D. R.".
- Sylvesters_sequence hasPhotoCollection Sylvesters_sequence.
- Sylvesters_sequence last "Curtiss".
- Sylvesters_sequence title "Sylvester's Sequence".
- Sylvesters_sequence urlname "SylvestersSequence".
- Sylvesters_sequence wikiPageUsesTemplate Template:Cite_arxiv.
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- Sylvesters_sequence wikiPageUsesTemplate Template:Good_article.
- Sylvesters_sequence wikiPageUsesTemplate Template:Harvs.
- Sylvesters_sequence wikiPageUsesTemplate Template:Harvtxt.
- Sylvesters_sequence wikiPageUsesTemplate Template:Mathworld.
- Sylvesters_sequence wikiPageUsesTemplate Template:OEIS.
- Sylvesters_sequence wikiPageUsesTemplate Template:Refbegin.
- Sylvesters_sequence wikiPageUsesTemplate Template:Refend.
- Sylvesters_sequence wikiPageUsesTemplate Template:Reflist.
- Sylvesters_sequence wikiPageUsesTemplate Template:Sfnp.
- Sylvesters_sequence wikiPageUsesTemplate Template:Unsolved.
- Sylvesters_sequence year "1922".
- Sylvesters_sequence subject Category:Egyptian_fractions.
- Sylvesters_sequence subject Category:Integer_sequences.
- Sylvesters_sequence subject Category:Mathematical_series.