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

%I A377421 #36 Nov 18 2024 22:31:03
%S A377421 6,10,11,12,13,14,20,22,23,24,25,26,28,29,34,37,40,41,43,44,46,47,48,
%T A377421 50,52,53,55,56,58,61,62,67,68,71,74,77,80,82,83,86,88,91,92,94,96,97,
%U A377421 100,101,104,106,110,112,113,115,116,121,122,124,131,134,136,142
%N A377421 Numbers whose binary reversal is prime and unequal to the original number.
%C A377421 Contains A080790 and p*2^i for all primes p in A074832 union A080790 and i > 0. - _Michael S. Branicky_, Oct 29 2024
%H A377421 James C. McMahon, <a href="/A377421/b377421.txt">Table of n, a(n) for n = 1..10000</a>
%F A377421 a = A204232 - A006995 (as sets). - _Michael S. Branicky_, Oct 29 2024
%e A377421 6 = 110_2 is a term since reversed it is 011_2 = 3 which is prime.
%e A377421 7 = 111_2 is not a term since base 2 palindromic numbers are not included.
%t A377421 Select[Range[142],PrimeQ[r=FromDigits[Reverse[IntegerDigits[#,2]],2]]&&r!=#&] (* _James C. McMahon_, Nov 18 2024 *)
%o A377421 (Python)
%o A377421 from sympy import isprime
%o A377421 def ok(n): return (b:=bin(n)[2:]) != (br:=b[::-1]) and isprime(int(br, 2))
%o A377421 print([k for k in range(1, 143) if ok(k)]) # _Michael S. Branicky_, Oct 28 2024
%o A377421 (Python) # alternate program constructing terms directly from primes
%o A377421 from sympy import primerange
%o A377421 def auptobits(maxbits):
%o A377421     alst = []
%o A377421     for p in primerange(3, 1<<maxbits):
%o A377421         b = bin(p)[2:]; br = b[::-1]; t = int(br, 2)
%o A377421         if br != b: alst.append(t)
%o A377421         alst.extend(t<<i for i in range(1, maxbits-len(br)+1))
%o A377421     return sorted(alst)
%o A377421 print(auptobits(8)) # _Michael S. Branicky_, Oct 29 2024
%Y A377421 Supersequence of A080790.
%Y A377421 Cf. A030101, A006995, A074832, A204232.
%K A377421 nonn,base
%O A377421 1,1
%A A377421 _Simon R Blow_, Oct 27 2024