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Search: id:A140889
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| A140889 |
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Lengths of runs of consecutive primes and composites in A008364. |
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+0
1
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| 1, 26, 1, 4, 1, 5, 1, 3, 1, 4, 1, 1, 1, 6, 1, 1, 1, 7, 1, 1, 1, 4, 2, 2, 1, 4, 1, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 4, 1, 1, 1, 2, 1, 3, 1, 2, 3, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 3, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 2, 2, 1, 1, 1, 2, 2, 1, 5, 2, 4, 2, 4, 3, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Primes can be classified according to their remainder modulo 2*3*5: remainder 1 (A073102), 11..113 (primes), 121 (composite), 127..139 (primes), 143 (composite), 149..167 (primes), 169 (composite), 173..181 (primes), 187 (composite), 191..199 (primes), or 209 (composite). In the sequence A008364 of allnumbers (prim orcomposite) in any of these remainder classes, we look for runs of numbers that are successively prime orcompsite and place the lengths of these runs in this sequence.
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EXAMPLE
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Groups of runs in A008364 are (1), (11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113), (121), (127, 131, 137, 139), (143), (149, 151, ... ), which is 1 composite followed by 26 primes followed by 1 composite followed by 4 primes etc.
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CROSSREFS
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Cf. A140378.
Sequence in context: A040691 A040690 A040689 this_sequence A040693 A040692 A040694
Adjacent sequences: A140886 A140887 A140888 this_sequence A140890 A140891 A140892
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 06 2008
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