A377421 Numbers whose binary reversal is prime and unequal to the original number.

6, 10, 11, 12, 13, 14, 20, 22, 23, 24, 25, 26, 28, 29, 34, 37, 40, 41, 43, 44, 46, 47, 48, 50, 52, 53, 55, 56, 58, 61, 62, 67, 68, 71, 74, 77, 80, 82, 83, 86, 88, 91, 92, 94, 96, 97, 100, 101, 104, 106, 110, 112, 113, 115, 116, 121, 122, 124, 131, 134, 136, 142

Offset

1,1

Comments

Contains A080790 and p*2^i for all primes p in A074832 union A080790 and i > 0. - Michael S. Branicky, Oct 29 2024

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Formula

a = A204232 - A006995 (as sets). - Michael S. Branicky, Oct 29 2024

Example

6 = 110_2 is a term since reversed it is 011_2 = 3 which is prime.
7 = 111_2 is not a term since base 2 palindromic numbers are not included.

Mathematica

Select[Range[142], PrimeQ[r=FromDigits[Reverse[IntegerDigits[#, 2]], 2]]&&r!=#&] (* James C. McMahon, Nov 18 2024 *)

Prog

(Python)
from sympy import isprime
def ok(n): return (b:=bin(n)[2:]) != (br:=b[::-1]) and isprime(int(br, 2))
print([k for k in range(1, 143) if ok(k)]) # Michael S. Branicky, Oct 28 2024
(Python) # alternate program constructing terms directly from primes
from sympy import primerange
def auptobits(maxbits):
    alst = []
    for p in primerange(3, 1<<maxbits):
        b = bin(p)[2:]; br = b[::-1]; t = int(br, 2)
        if br != b: alst.append(t)
        alst.extend(t<<i for i in range(1, maxbits-len(br)+1))
    return sorted(alst)
print(auptobits(8)) # Michael S. Branicky, Oct 29 2024

Crossrefs

Supersequence of A080790.

Cf. A030101, A006995, A074832, A204232.

Sequence in context: A284302 A284350 A333410 * A107014 A206036 A349761

Adjacent sequences: A377418 A377419 A377420 * A377422 A377423 A377424

Keyword

nonn,base

Author

Simon R Blow, Oct 27 2024

Status

approved