A286333 Primes p where all the cyclic shifts of their digits to the left also produce primes except the last one before reaching p again.

19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 101, 103, 107, 127, 149, 157, 163, 181, 191, 307, 317, 331, 359, 367, 701, 709, 727, 739, 757, 761, 787, 797, 907, 937, 941, 947, 983, 1103, 1109, 1123, 1181, 1301, 1319, 1327, 1949, 1951, 1979, 1987, 1993, 3121, 3187, 3361, 3373, 3701

Offset

1,1

Comments

a(144) = 733793111393, a(145) is larger than 10^16 (if it exists).

Can be considered as primitive terms of A270083, i.e. terms in A270083 can be obtained by cyclic shifts of the digits of terms in this sequence (and leading zeros are not allowed). - Chai Wah Wu, May 21 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..144

Example

1123 is a member as all the cyclic shifts of its digits to the left result are primes (1231, 2311) except the last one (3112) before reaching the original prime.

Mathematica

cyclDigs[k_]:= FromDigits/@ NestList[RotateLeft, IntegerDigits[k], IntegerLength[k]-1]; lftSftNearCircPrmsInBtw[m_, n_]:= ParallelMap[If[ AllTrue[Most[cyclDigs[#]], PrimeQ] && Not@ PrimeQ[Last[cyclDigs[#]]], #, Nothing] &, Prime @ Range[PrimePi[m], PrimePi[n]]];
lftSftNearCircPrmsInBtw[19, 10^7]

Prog

(Python)
from itertools import product
from sympy import isprime
A286333_list = []
for l in range(14):
    for w in product('1379', repeat=l):
        for d in '0123456789':
            for t in '1379':
                s = ''.join(w)+d+t
                n = int(s)
                for i in range(l+1):
                    if not isprime(int(s)):
                        break
                    s = s[1:]+s[0]
                else:
                    if n > 10 and not isprime(int(s)):
                        A286333_list.append(n) # Chai Wah Wu, May 21 2017

Crossrefs

Cf. A270083 (subsequence of), A286415.

Sequence in context: A309360 A151768 A270083 * A076056 A068654 A286415

Adjacent sequences: A286330 A286331 A286332 * A286334 A286335 A286336

Keyword

nonn,base

Author

Mikk Heidemaa, May 07 2017

Status

approved