cp's OEIS Frontend

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.

%I A274134 #15 Sep 16 2024 20:31:27
%S A274134 3,7,11,31,43,67,79,127,131,139,167,191,211,223,227,307,331,367,487,
%T A274134 523,631,691,743,751,883,971,1039,1087,1399,2063,2083,2143,2179,2239,
%U A274134 2267,2287,2347,2411,2423,2503,2531,2543,2591,2687,2731,2803,2819,2927,2939,2963
%N 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.
%C A274134 a(n) mod 4 = 3.
%t A274134 Select[Prime@ Range@ 430, And[PrimeQ@ FromDigits[RotateLeft@ #, 2], PrimeQ@ FromDigits[RotateRight@ #, 2]] &@ IntegerDigits[#, 2] &] (* _Michael De Vlieger_, Jun 22 2016 *)
%o A274134 (Python)
%o A274134 from sympy import isprime
%o A274134 for n in range(3, 10000, 2):
%o A274134     if not isprime(n): continue
%o A274134     BL = len(bin(n))-2
%o A274134     x = (n>>1) + ((n&1) << (BL-1))   # A038572(n)
%o A274134     if not isprime(x): continue
%o A274134     y = (n*2) - (1<<BL) + 1   # A006257(n)  for n>0
%o A274134     if not isprime(y): continue
%o A274134     print(str(n), end=', ')
%Y A274134 Cf. A000040, A006257, A038572.
%K A274134 nonn,base
%O A274134 1,1
%A A274134 _Alex Ratushnyak_, Jun 10 2016