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

1,1

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).

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

Example

For example 1259 becomes 6521 under such a rotation.

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 *)

Prog

(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

Crossrefs

Cf. A007500, A055387, A018847.

Sequence in context: A276591 A051653 A106015 * A179632 A093871 A033263

Adjacent sequences: A178313 A178314 A178315 * A178317 A178318 A178319

Keyword

nonn,base,changed

Author

David Nacin, May 24 2010

Status

approved