This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117773 #32 Feb 16 2025 08:33:00
%S A117773 0,1,2,0,2,0,3,0,3,0,7,0,12,0,23,0,40,0,94,0,142,0,271,0,480,0,856,0,
%T A117773 1721,0,3099,0,5572,0,10799,0,20782,0,39468,0,72672,0,139867,0,274480,
%U A117773 0,520376,0,986318,0,1914097,0,3726617,0,7107443,0,13682325,0,26430797,0,51412565,0,99204128,0,190457946,0
%N A117773 Number of palindromic primes in base 2 with exactly n binary digits.
%C A117773 Every palindrome with an even number of digits is divisible by 11 (in base 2), i.e., by 3 in base 10, and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits, namely 11_2 = 3_{10}.
%H A117773 Chai Wah Wu, <a href="/A117773/b117773.txt">Table of n, a(n) for n = 1..76</a>
%H A117773 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.
%H A117773 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>.
%t A117773 Array[If[And[OddQ[#], # > 1], 0, Count[Prime@ Range[PrimePi[2^#] - Boole[# == 1] + 1, PrimePi[2^(# + 1) - 1]], _?(PalindromeQ[IntegerDigits[#, 2]] &)]] &, 25, 0] (* _Michael De Vlieger_, Sep 29 2023 *)
%Y A117773 Cf. A016041, A117697, A095741.
%K A117773 nonn,base
%O A117773 1,3
%A A117773 _Martin Renner_, Apr 15 2006
%E A117773 a(23)-a(40) from _Donovan Johnson_, Dec 02 2009
%E A117773 a(41)-a(66) from _Martin Raab_, Oct 20 2015