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%I #25 Apr 10 2021 21:10:47
%S 3,5,7,313,7284717174827,390714505091666190505417093
%N Primes that are palindromic in bases 2 and 10.
%H P. De Geest, <a href="http://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>
%e 313_10 = 100111001_2. - _Jon E. Schoenfield_, Apr 10 2021
%t Select[Prime[Range[10!]], IntegerDigits[#]==Reverse[IntegerDigits[#]] && IntegerDigits[#,2]==Reverse[IntegerDigits[#,2]]&] (* _Vladimir Joseph Stephan Orlovsky_, Dec 30 2010 *)
%t p = Sort[Reap[Do[d=IntegerDigits[n]; p1=FromDigits[Join[Most[d], Reverse[d]]]; p2=FromDigits[Join[d, Reverse[d]]]; If[IntegerDigits[p1, 2] == Reverse[IntegerDigits[p1, 2]], Sow[p1]]; If[IntegerDigits[p2, 2] == Reverse[IntegerDigits[p2, 2]], Sow[p2]], {n, 0, 9999999}]][[2, 1]]]; Select[p, PrimeQ]
%Y Cf. A002385 (palindromic primes), A007632 (palindromes in bases 2 and 10).
%K nonn,hard,base
%O 1,1
%A _Patrick De Geest_, Aug 15 1998
%E a(6) (from A007632) added by _T. D. Noe_, Dec 31 2010
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