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A286415 Primes p where all the cyclic shifts of their digits to the right also produce primes except the last one before reaching p again. 3
19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 173, 271, 277, 313, 379, 397, 419, 479, 491, 571, 577, 593, 617, 631, 673, 811, 839, 877, 911, 977, 1777, 1913, 2131, 2311, 2377, 2399, 2713, 2791, 2939, 2971, 4177, 4339, 4919, 4993, 5119, 5791, 6133, 6737, 6997, 7193, 7333, 7919, 8111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..125

EXAMPLE

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.

MATHEMATICA

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]]];

rgtSftNearCircPrmsInBtw[19, 10^7]

PROG

(Python)

from itertools import product

from sympy import isprime

A286415_list = []

for l in range(1, 15):

    for d in '123456789':

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

            s = d+''.join(w)

            n = int(s)

            for i in range(l):

                if not isprime(int(s)):

                    break

                s = s[-1]+s[:-1]

            else:

                if not isprime(int(s)):

                    A286415_list.append(n) # Chai Wah Wu, May 21 2017

CROSSREFS

Cf. A270083 (subsequence of), A286333.

Sequence in context: A286333 A076056 A068654 * A305835 A019384 A088987

Adjacent sequences:  A286412 A286413 A286414 * A286416 A286417 A286418

KEYWORD

nonn,base

AUTHOR

Mikk Heidemaa, May 08 2017

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)