A389481 Primes that remain prime when their binary digits are rotated once to the right.

3, 7, 11, 31, 43, 59, 67, 79, 127, 131, 139, 167, 191, 199, 211, 223, 227, 283, 307, 331, 367, 463, 487, 523, 571, 599, 619, 631, 683, 691, 739, 743, 751, 859, 883, 911, 919, 971, 1019, 1039, 1051, 1087, 1171, 1279, 1291, 1399, 1447, 1459, 1471, 1531, 1699, 1951, 1987

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Prime 7 = 111_2 is a term since rotating its binary digits once to the right yields 111_2 = 7 again, prime.
Prime 43 = 101011_2 is a term since rotating its binary digits once to the right yields 110101_2 = 53, prime.
Prime 5 = 101_2 is not a term since rotating its binary digits once to the right yields 110_2 = 6, not prime.

Maple

filter:=  proc(n) isprime(n) and isprime(floor(n/2) + 2^ilog2(n)) end proc:
select(filter, [seq(i, i=3..2000, 4)]); # Robert Israel, Oct 06 2025

Mathematica

Select[Prime[Range[300]], PrimeQ[FromDigits[RotateRight[IntegerDigits[#, 2]], 2]]&] (* James C. McMahon, Oct 15 2025 *)

Prog

(Python)
from sympy import isprime
def ok(n): return isprime(n) and isprime(int((b:=bin(n)[2:])[-1]+b[:-1], 2))
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Oct 05 2025
(PARI) isok(p)=isprime(p) && bittest(p, 0) && isprime(p\2 + 2^logint(p, 2)) \\ Andrew Howroyd, Oct 05 2025

Crossrefs

Supersequence of A389139.

Subset of A002145.

Cf. A004676.

Cf. A234901 (same in base 10).

Sequence in context: A213740 A267357 A152084 * A274134 A131588 A361680

Adjacent sequences: A389478 A389479 A389480 * A389482 A389483 A389484

Keyword

nonn,base

Author

Rhys Feltman, Oct 05 2025

Extensions

More terms from Michael S. Branicky, Oct 05 2025

Status

approved