A389139 Primes that remain prime when their digits are rotated once to the right in both binary and decimal.

3, 7, 11, 31, 79, 131, 199, 571, 631, 911, 919, 971, 1039, 1171, 1279, 1291, 1531, 2011, 2311, 2591, 2819, 2939, 2971, 3119, 3191, 3499, 3719, 3919, 4091, 4231, 5791, 6991, 8011, 8311, 8599, 8839, 9011, 9871, 10099, 10271, 10691, 10799, 10979, 11131, 11279, 11299

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

Prime 131 = 10000011_2 is a term since 113 and 11000001_2 = 197 are prime.
Prime 5 = 101_2 is not a term because 110_2 = 6 is not prime.

Mathematica

prQ[p_, b_] := PrimeQ[FromDigits[StringRotateRight[IntegerString[p, b]], b]];
Select[Prime[Range[2000]], prQ[#, 2] && prQ[#, 10] &] (* Paolo Xausa, Sep 29 2025 *)

Prog

(Python)
from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s, b = str(n), bin(n)[2:]
    return isprime(int(s[-1]+s[:-1])) and isprime(int(b[-1]+b[:-1], 2))
print([k for k in range(11300) if ok(k)]) # Michael S. Branicky, Sep 24 2025

Crossrefs

Intersection of A234901 and A389481.

Sequence in context: A091938 A333424 A186893 * A051919 A119175 A038913

Adjacent sequences: A389136 A389137 A389138 * A389140 A389141 A389142

Keyword

nonn,base

Author

Rhys Feltman, Sep 24 2025

Status

approved