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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.
2
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
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
KEYWORD
nonn,base
AUTHOR
Mikk Heidemaa, May 07 2017
STATUS
approved