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Search: id:A080340
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| A080340 |
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First known infinite sequence containing no odd integer of the form 2^m+p (p prime). |
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+0
2
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| 7629217, 18814027, 29998837, 41183647, 52368457, 63553267, 74738077, 85922887, 97107697, 108292507, 119477317, 130662127, 141846937, 153031747, 164216557, 175401367, 186586177, 197770987, 208955797, 220140607, 231325417, 242510227
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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To a question of Romanoff: Are there infinitely many odd integers not of the form 2^m+p where p is prime? Erdos answered Yes in 1950 by constructing the present sequence, an infinite arithmetic sequence, using a system of congruences.
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REFERENCES
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P. Erdos, "On integers of form 2^n+p and some related problems", Summa Brasil Math.11 (1950), pp. 1-11
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LINKS
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Tanya Khovanova, Recursive Sequences
T. Zamojski, Survey on covering congruences.
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FORMULA
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a(n)=n*11184810+7629217
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CROSSREFS
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Adjacent sequences: A080337 A080338 A080339 this_sequence A080341 A080342 A080343
Sequence in context: A105003 A102334 A043668 this_sequence A124416 A032430 A015391
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 19 2003
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