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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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9
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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
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OFFSET
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1,1
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COMMENTS
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Sequence A016038 is identical up to four additional terms: 0, 1, 2, 3; see there for more information.
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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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[4, 1500], And@@(#!=Reverse[#]&/@Table[IntegerDigits[#, b], {b, 2, #/2}])&] (* Harvey P. Dale, May 22 2013 *)
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PROG
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(PARI) is(n)=!for(b=2, n\2, Vecrev(d=digits(n, b))==d&&return)&&n>3 \\ M. F. Hasler, Sep 08 2015
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CROSSREFS
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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