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A002072
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a(n) = smallest number m such that for all i>m, either i or i+1 has a prime factor > prime(n).
(Formerly M4560 N1942)
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7
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1, 8, 80, 4374, 9800, 123200, 336140, 11859210, 11859210, 177182720, 1611308699, 3463199999, 63927525375, 421138799639, 1109496723125, 1453579866024, 20628591204480, 31887350832896, 31887350832896, 119089041053696, 2286831727304144, 9591468737351909375, 9591468737351909375, 9591468737351909375, 9591468737351909375, 9591468737351909375, 19316158377073923834000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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E. F. Ecklund and R. B. Eggleton, Prime factors of consecutive integers, Amer. Math. Monthly, 79 (1972), 1082-1089.
D. H. Lehmer, On a problem of Stormer, Ill. J. Math., 8 (1964), 57-69.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..27.
Don Reble, Python program
Wikipedia, Stormer's Theorem
Jim White, Results to P = 173
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EXAMPLE
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31887350832897=3^9*7*37*41^2*61^2, 31887350832896=2^8*13*19*23*29^4*31, this number appears twice because there is no pair of numbers with max. factor = 67 that is larger than this number.
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PROG
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Program in C written by R. Gerbicz, modified by Fred Schneider and Jim White.
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CROSSREFS
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Cf. A002071, A003032, A003033. Equals A117581(n) - 1.
Cf. A122463, A145606.
Sequence in context: A057707 A222671 A145606 * A193943 A067449 A078292
Adjacent sequences: A002069 A002070 A002071 * A002073 A002074 A002075
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Jan 11 2005
a(18)-a(26) from Fred Schneider (frederick.william.schneider(AT)gmail.com), Sep 09 2006
Corrected and extended by Andrey V. Kulsha, Aug 10 2011, according to Jim White's computations
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STATUS
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approved
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