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%I #21 Sep 29 2023 12:00:39
%S 3,20,101,508,3053,20053,141772,1045600,8038954,63830588,518935134,
%T 4311185894
%N Number of binary reversal primes less than 10^n.
%C MathPages counts 1 as being a binary reversal prime whereas the title would exclude it, therefore their count exceeds this count by one.
%H Kevin S. Brown's Mathpages, <a href="http://www.mathpages.com/home/kmath362.htm">Reflective and Cyclic Sets of Primes</a>
%H Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, <a href="https://arxiv.org/abs/2309.11380">Reversible primes</a>, arXiv:2309.11380 [math.NT], 2023. See p. 34.
%t f[n_] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]; NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; c = 0; k = 1; Do[ While[k = NextPrim[k]; k < 10^n, If[ PrimeQ[ f[k]], c++ ]]; k--; Print[c], {n, 16}]
%o (Python)
%o from sympy import isprime, primerange
%o def is_bin_rev_prime(n): return isprime(int(bin(n)[2:][::-1], 2))
%o def a(n): return sum(is_bin_rev_prime(p) for p in primerange(1, 10**n))
%o print([a(n) for n in range(1, 7)]) # _Michael S. Branicky_, Mar 20 2021
%K nonn,base,hard,more
%O 1,1
%A _Robert G. Wilson v_, Sep 09 2002
%E a(10)-a(11) from _Chai Wah Wu_, Oct 09 2018
%E a(12) from _Chai Wah Wu_, Oct 10 2018
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