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

1,1

Comments

a(n) mod 4 = 3.

Links

Table of n, a(n) for n=1..50.

Mathematica

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

Prog

(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<<BL) + 1   # A006257(n)  for n>0
    if not isprime(y): continue
    print(str(n), end=', ')

Crossrefs

Cf. A000040, A006257, A038572.

Sequence in context: A213740 A267357 A152084 * A131588 A361680 A091938

Adjacent sequences: A274131 A274132 A274133 * A274135 A274136 A274137

Keyword

nonn,base

Author

Alex Ratushnyak, Jun 10 2016

Status

approved