

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 < p1. Hence to find nonpalindromic 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


REFERENCES

R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425428.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


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 A302428
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



