A286415 - OEIS

%I #28 Oct 05 2020 14:08:24

%S 19,23,29,41,43,47,53,59,61,67,83,89,173,271,277,313,379,397,419,479,

%T 491,571,577,593,617,631,673,811,839,877,911,977,1777,1913,2131,2311,

%U 2377,2399,2713,2791,2939,2971,4177,4339,4919,4993,5119,5791,6133,6737,6997,7193,7333,7919,8111

%N Primes p where all the cyclic shifts of their digits to the right also produce primes except the last one before reaching p again.

%C a(125)=937337931113, a(126) is larger than 10^16 (if it exists).

%H Chai Wah Wu, <a href="/A286415/b286415.txt">Table of n, a(n) for n = 1..125</a>

%e 2131 is a member as all the cyclic shifts of its digits to the right result in primes (1213, 3121) except the last one (1312) before reaching the original prime.

%t cyclDigs[k_]:= FromDigits/@ NestList[RotateRight, IntegerDigits[k], IntegerLength[k]-1]; rgtSftNearCircPrmsInBtw[m_, n_]:= ParallelMap[ If[AllTrue[Most[cyclDigs[#]], PrimeQ] && Not@ PrimeQ[Last[cyclDigs[#]]], #, Nothing] &, Prime @ Range[PrimePi[m], PrimePi[n]]];

%t rgtSftNearCircPrmsInBtw[19, 10^7]

%t cspQ[n_]:=Module[{t=PrimeQ[FromDigits/@Table[RotateRight[IntegerDigits[ n],k],{k,IntegerLength[n]-1}]]},Last[t]==False&&Union[Most[t]]=={True}]; Join[ {19,23,29,41,43,47,53,59,61,67,83,89},Select[ Prime[ Range[ 26,1100]],cspQ]] (* _Harvey P. Dale_, Oct 05 2020 *)

%o (Python)

%o from itertools import product

%o from sympy import isprime

%o A286415_list = []

%o for l in range(1,15):

%o     for d in '123456789':

%o         for w in product('1379',repeat=l):

%o             s = d+''.join(w)

%o             n = int(s)

%o             for i in range(l):

%o                 if not isprime(int(s)):

%o                     break

%o                 s = s[-1]+s[:-1]

%o             else:

%o                 if not isprime(int(s)):

%o                     A286415_list.append(n) # _Chai Wah Wu_, May 21 2017

%Y Cf. A270083 (subsequence of), A286333.

%K nonn,base

%O 1,1

%A _Mikk Heidemaa_, May 08 2017