|
%I #19 Aug 11 2024 14:41:30
%S 2,13,23,151,173,233,757,937,1093,1249,1429,1487,1667,1733,1823,1913,
%T 1979,2069,8389,9103,10111,12301,14951,16673,16871,18593,60103,60913,
%U 61507,63127,69697,73243,78979,80599,82003,82813,83407,85027
%N Palindromic primes in base 3.
%C Intersection of A000040 and A014190. - _Michel Marcus_, Aug 19 2015
%H Chai Wah Wu, <a href="/A029971/b029971.txt">Table of n, a(n) for n = 1..3004</a>
%H P. De Geest, <a href="https://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>
%p N:= 14: # to get all terms < 3^N
%p Res:= 2:
%p digrev:=proc(n) local L;
%p L:= convert(n,base,3);
%p add(L[-i]*3^(i-1),i=1..nops(L))
%p end proc;
%p for d from 2 to N do
%p if d::even then
%p m:= d/2;
%p Res:= Res, op(select(isprime,[seq](n*3^m + digrev(n), n=3^(m-1)..3^m-1)));
%p else
%p m:= (d-1)/2;
%p Res:= Res, op(select(isprime,[seq](seq(n*3^(m+1)+y*3^m+digrev(n),
%p y=0..2), n=3^(m-1)..3^m-1)));
%p fi
%p od:
%p Res; # _Robert Israel_, Aug 19 2015
%t Do[s = RealDigits[n, 3][[1]]; If[PrimeQ[n], If[FromDigits[s] == FromDigits[Reverse[s]], Print[n]]], {n, 1, 8500}]
%t Select[Prime[Range[8300]], Reverse[x = IntegerDigits[#, 3]] == x &] (* _Jayanta Basu_, Jun 23 2013 *)
%o (PARI) lista(nn) = forprime(p=2, nn, if ((d=digits(p,3)) && (Vecrev(d)==d), print1(p, ", "))); \\ _Michel Marcus_, Aug 19 2015
%Y Cf. A117698 (in base 3), A014190.
%K nonn,base
%O 1,1
%A _Patrick De Geest_
|
