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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.
0
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.
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
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Jun 10 2016
STATUS
approved