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Search: id:A111166
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| A111166 |
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Let p(n) denote the n-th prime; p(n) is in the sequence iff p(n)/(p(n+1)-p(n)) is a record. |
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1
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| 2, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Conjecture: Except for first term, the sequence coincides with A001359. This is true for all primes < 2*10^7.
Conjecture: Except for first term, the sequence coincides with A001359. This is true for all primes < 7*10^16. Let n >= 2 be an integer, N +- 1 and M +- 1 two consecutive twin pairs where M>n*N. Finding a counterexample is the same as finding two consecutive primes P1 and P2 with n*N<P1<M and P2-P1 <= n. However, such gaps are unknown even for n=2.
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EXAMPLE
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a(0)=2 and the record is 2/(3-2)=2; a(1)<>3 because 3/(5-3)=1.5; a(1)=5 because 5/(7-5)=2.5
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CROSSREFS
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Cf. A001359.
Sequence in context: A023222 A007491 A124850 this_sequence A064337 A076873 A089440
Adjacent sequences: A111163 A111164 A111165 this_sequence A111167 A111168 A111169
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KEYWORD
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easy,nonn
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AUTHOR
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Bernardo Boncompagni (redgolpe(AT)redgolpe.com), Oct 21 2005
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