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 A047811 Numbers n >= 4 that are not palindromic in any base b, 2 <= b <= n/2. 9
 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; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425-428. FORMULA a(n) = A016038(n+4) for all n. - M. F. Hasler, Sep 08 2015 MATHEMATICA Select[Range[4, 1500], And@@(#!=Reverse[#]&/@Table[IntegerDigits[#, b], {b, 2, #/2}])&] (* Harvey P. Dale, May 22 2013 *) PROG (PARI) is(n)=!for(b=2, n\2, Vecrev(d=digits(n, b))==d&&return)&&n>3 \\ M. F. Hasler, Sep 08 2015 CROSSREFS Cf. A016038, A050812, A050813. Cf. A135549. Sequence in context: A058579 A022318 A291916 * A244010 A154145 A327553 Adjacent sequences: A047808 A047809 A047810 * A047812 A047813 A047814 KEYWORD nonn,base,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS Extended (and corrected) by Patrick De Geest, Oct 15 1999 Minor edits by M. F. Hasler, Sep 08 2015 STATUS approved

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Last modified December 8 15:17 EST 2023. Contains 367680 sequences. (Running on oeis4.)