A274134 Primes p such that both ror(p) and rol(p) are also primes, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left.

3, 7, 11, 31, 43, 67, 79, 127, 131, 139, 167, 191, 211, 223, 227, 307, 331, 367, 487, 523, 631, 691, 743, 751, 883, 971, 1039, 1087, 1399, 2063, 2083, 2143, 2179, 2239, 2267, 2287, 2347, 2411, 2423, 2503, 2531, 2543, 2591, 2687, 2731, 2803, 2819, 2927, 2939, 2963

Offset: 1

Author

Alex Ratushnyak, Jun 10 2016

Keywords

• nonn
• base

Comments

a(n) mod 4 = 3.

Crossrefs

Cf. A000040, A006257, A038572.

Programs

Mathematica

Select[Prime@ Range@ 430, And[PrimeQ@ FromDigits[RotateLeft@ #, 2], PrimeQ@ FromDigits[RotateRight@ #, 2]] &@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Jun 22 2016 *)

Python

from sympy import isprime
for n in range(3, 10000, 2):
    if not isprime(n): continue
    BL = len(bin(n))-2
    x = (n>>1) + ((n&1) << (BL-1))   # A038572(n)
    if not isprime(x): continue
    y = (n*2) - (1<A006257(n)  for n>0
    if not isprime(y): continue
    print(str(n), end=', ')