cp's OEIS Frontend

A068653 Composite numbers such that every cyclic shift (other than the number itself) gives a prime.

%I A068653 #24 Dec 07 2018 17:29:56
%S A068653 14,16,20,30,32,34,35,38,50,70,74,76,91,92,95,98,110,118,119,133,170,
%T A068653 176,194,310,316,398,710,712,715,730,731,736,772,775,778,779,790,793,
%U A068653 794,914,935,970,973,1118,1130,1195,1312,1336,1370,1774,1937,3110,3112
%N A068653 Composite numbers such that every cyclic shift (other than the number itself) gives a prime.
%C A068653 Single-digit numbers are excluded. There are only 144 terms up through 10 million. - _Harvey P. Dale_, Sep 12 2014
%H A068653 Chai Wah Wu, <a href="/A068653/b068653.txt">Table of n, a(n) for n = 1..148</a> a(n) for n = 1..144 from Harvey P. Dale.
%e A068653 176 is a term as the two cyclic shifts other than the number itself, 761 and 617, are primes.
%t A068653 LiQ[n_] := Module[{s=0}, li1=IntegerDigits[n]; k=Length[li1]; t={li1}; Do[li1=RotateLeft[li1]; AppendTo[t,li1], {i,k-1}]; If[Length[Select[Table[FromDigits[p],{p,t}], PrimeQ]] == k-1, s=1]; s]; t1={}; Do[If[!PrimeQ[i] && LiQ[i]==1, AppendTo[t1,i]], {i,10,3112}]; t1 (* _Jayanta Basu_, May 03 2013 *)
%t A068653 cppQ[n_]:=Module[{c=FromDigits/@NestList[RotateLeft[#]&,IntegerDigits[n], IntegerLength[ n]-1]},CompositeQ[c[[1]]]&&AllTrue[Rest[c],PrimeQ]]; Select[ Range[10,5000],cppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 12 2014 *)
%o A068653 (Python)
%o A068653 from itertools import product
%o A068653 from sympy import isprime
%o A068653 A068653_list = []
%o A068653 for l in range(1,9):
%o A068653     for m in product(('1379' if l > 1 else '123579'),repeat=l):
%o A068653         for d in '0123456789':
%o A068653             s = ''.join(m)+d
%o A068653             n = int(s)
%o A068653             if not isprime(n):
%o A068653                 for k in range(len(s)-1):
%o A068653                     s = s[1:]+s[0]
%o A068653                     if not isprime(int(s)):
%o A068653                         break
%o A068653                 else:
%o A068653                     A068653_list.append(n) # _Chai Wah Wu_, May 06 2017
%Y A068653 Cf. A003459, A068652.
%K A068653 base,nonn
%O A068653 1,1
%A A068653 _Amarnath Murthy_, Feb 28 2002
%E A068653 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 21 2002