A178316 Primes whose digital rotation is still prime.

2, 5, 11, 19, 61, 101, 109, 151, 181, 199, 601, 619, 659, 661, 1019, 1021, 1061, 1091, 1109, 1129, 1151, 1181, 1201, 1229, 1259, 1291, 1511, 1559, 1601, 1609, 1621, 1669, 1699, 1811, 1901, 1999, 6011, 6091, 6101, 6199, 6211, 6221, 6229, 6521, 6551, 6569

Offset: 1

Author

David Nacin, May 24 2010

Keywords

• nonn
• base

Comments

This means if written as in a digital clock and rotated 180 degrees around the center the result is also prime (possibly a different prime).

Examples

			For example 1259 becomes 6521 under such a rotation.
		

References

• Guy, R. K., Unsolved Problems in Number Theory, p 15 This sequence is related to the palindromic primes with symmetries as in Guy's book.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007500, A055387, A018847.

Programs

Mathematica

Select[Range[6570],PrimeQ[#]&&PrimeQ[FromDigits[Reverse[IntegerDigits[#]/.{6->9,9->6}]]]&&ContainsOnly[IntegerDigits[#],{0,1,2,5,6,8,9}]&] (* James C. McMahon, Apr 09 2024 *)

Python

from itertools import count, islice, product
from sympy import isprime
def A178316_gen():
    yield from (2,5)
    r = ''.maketrans('69','96')
    for l in count(1):
        for a in '125689':
            for d in product('0125689',repeat=l):
                s = a+''.join(d)
                m = int(s)
                if isprime(m) and isprime(int(s[::-1].translate(r))):
                    yield m
A178316_list = list(islice(A178316_gen(),40)) # Chai Wah Wu, Apr 09 2024