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A140889
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Lengths of runs of consecutive primes and composites in A008364.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Primes can be classified according to their remainder modulo 210: 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 all numbers (prime or composite) in any of these remainder classes, we look for runs of numbers that are successively prime or composite and place the lengths of these runs in this sequence.
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EXAMPLE
| 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
| Cf. A140378.
Sequence in context: A040691 A040690 A040689 * A040693 A040692 A040694
Adjacent sequences: A140886 A140887 A140888 * A140890 A140891 A140892
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KEYWORD
| nonn
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 06 2008
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EXTENSIONS
| First number in the comment corrected and entries checked by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2010
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