A047811 Numbers n >= 4 that are not palindromic in any base b, 2 <= b <= n/2.

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

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