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

Author

Simon R Blow, Oct 27 2024

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Supersequence of A080790.

Cf. A030101, A006995, A074832, A204232.

Programs

Mathematica

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

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<Michael S. Branicky, Oct 29 2024

Formula

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