

A068652


Numbers such that every cyclic permutation is a prime.


18



2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993
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OFFSET

1,1


COMMENTS

The Sarcone link claims (erroneously) that after 319993 all terms are repunits.  N. J. A. Sloane, May 04 2017. The claim is obviously false, at least nine larger nonrepunit terms appear after 319993. They are, not surprisingly, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331.  Alexei Kourbatov, May 04 2017
See the closely related sequence A016114 for further information.  N. J. A. Sloane, May 04 2017


LINKS

Ray Chandler, Table of n, a(n) for n = 1..57
K. S. Brown, On General Palindromic Numbers
C. K. Caldwell, Circular Primes
P. De Geest, Circular Primes
H. Heinz, Prime Patterns (Illustration using 19937)
Gianni Sarcone, Tourbillonnants nombres premiers, Tangente Web Site, No date. The claim stated here is false (see comments above).


EXAMPLE

197 is a member as all the three cyclic permutations 197,971,719 are primes.


MATHEMATICA

fQ[p_] := Module[{b = IntegerDigits[p]}, And @@ Table[PrimeQ[FromDigits[b = RotateLeft[b]]], {Length[b]  1}]]; Select[Prime[Range[100000]], fQ] (* T. D. Noe, Mar 22 2012 *)
ecppQ[n_]:=AllTrue[FromDigits/@Table[RotateLeft[IntegerDigits[n], i], {i, IntegerLength[n]}], PrimeQ]; Select[Range[400000], ecppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 25 2015 *)


CROSSREFS

Cf. A003459, A016114, A091633.
Sequence in context: A107845 A234901 A090934 * A003459 A276132 A202264
Adjacent sequences: A068649 A068650 A068651 * A068653 A068654 A068655


KEYWORD

base,nonn,changed


AUTHOR

Amarnath Murthy, Feb 28 2002


EXTENSIONS

More terms from Martin Renner, Apr 10 2002


STATUS

approved



