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A002071
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Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime.
(Formerly M3386 N1366)
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9
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1, 4, 10, 23, 40, 68, 108, 167, 241, 345, 482, 653, 869, 1153, 1502
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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).
Stormer, Carl (1897). "Quelques theoremes sur l'equation de Pell x^2 - Dy^2 = +-1 et leurs applications". Skrifter Videnskabs-selskabet (Christiania), Mat.-Naturv. Kl. I (2).
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LINKS
| D. Eppstein, Smooth pairs.
D. Eppstein, Maple program
Wikipedia, Stormer's theorem
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CROSSREFS
| Cf. A002072.
Cf. A138180 (triangle of x values for each n).
Cf. A145604, A145605, A145606.
Sequence in context: A189596 A023378 A038423 * A024980 A002766 A008268
Adjacent sequences: A002068 A002069 A002070 * A002072 A002073 A002074
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KEYWORD
| nonn,nice,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and more terms from David Eppstein (eppstein(AT)ics.uci.edu), Mar 23 2007
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