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Search: id:A111943
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| A111943 |
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Increasing Cramer-Shanks-Granville ratios (p_{n+1}-p_n)/log(p_n)^2. |
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+0
3
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| 13, 23, 113, 1327, 31397, 370261, 2010733, 20831323, 25056082087, 2614941710599, 19581334192423, 218209405436543, 1693182318746371
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes less than 23 are anomalous and are excluded.
The sequence ends with Bertil Nyman's 1999 discovery.
Shanks conjecture is that the ratio will never reach 1.
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REFERENCES
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R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, A8.
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EXAMPLE
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Ratio, prime:
0.6103, 23
0.6264, 113
0.6575, 1327
0.6715, 31397
0.6812, 370261
0.7025, 2010733
0.7394, 20831323
0.7953, 25056082087
0.7975, 2614941710599
0.8177, 19581334192423
0.8311, 218209405436543
0.9206, 1693182318746371
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CROSSREFS
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Cf. A111870.
Adjacent sequences: A111940 A111941 A111942 this_sequence A111944 A111945 A111946
Sequence in context: A147443 A131447 A110196 this_sequence A039448 A089768 A018945
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KEYWORD
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nonn,hard
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), following emails from R. K. Guy and Ed Pegg, Jr., Nov 27 2005
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