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A047811
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Numbers n >= 4 that are not palindromic in any base b, 2<=b<=n/2.
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8
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4, 6, 11, 19, 47, 53, 79, 103, 137, 139, 149, 163, 167, 179, 223, 263, 269, 283, 293, 311, 317, 347, 359, 367, 389, 439, 491, 563, 569, 593, 607, 659, 739, 827, 853, 877, 977, 983, 997, 1019, 1049, 1061, 1187, 1213, 1237, 1367, 1433, 1439, 1447, 1459
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| See sequence A016038 for more information and four additional terms: 0, 1, 2, 3.
Note that no prime p is palindromic in base b for the range sqrt(p) < b < p-1. Hence to find non-palindromic primes, we need only examine bases up to floor(sqrt(p)), which greatly reduces the computational effort required. - T. D. Noe, Mar 01 2008
This sequence is mentioned in the paper by Richard Guy, in which he reports on unsolved problems. This problem came from Mario Borelli and Cecil B. Mast. The paper poses two questions about these numbers: (1) Can palindromic or nonpalindromic primes be otherwise characterized? and (2) What is the cardinality, or the density, of the set of palindromic primes? Of the set of nonpalindromic primes? - T. D. Noe, Apr 17 2011
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REFERENCES
| R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425-428.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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CROSSREFS
| Cf. A033868, A050812, A050813, A016038.
Cf. A135549.
Sequence in context: A197985 A058579 A022318 * A154145 A091280 A066155
Adjacent sequences: A047808 A047809 A047810 * A047812 A047813 A047814
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KEYWORD
| nonn,base,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Extended (and corrected) by Patrick De Geest (pdg(AT)worldofnumbers.com), Oct 15 1999.
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