A029971 Palindromic primes in base 3.

2, 13, 23, 151, 173, 233, 757, 937, 1093, 1249, 1429, 1487, 1667, 1733, 1823, 1913, 1979, 2069, 8389, 9103, 10111, 12301, 14951, 16673, 16871, 18593, 60103, 60913, 61507, 63127, 69697, 73243, 78979, 80599, 82003, 82813, 83407, 85027

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Intersection of A000040 and A014190. - Michel Marcus, Aug 19 2015

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..3004
• P. De Geest, World!Of Palindromic Primes

Crossrefs

Cf. A117698 (in base 3), A014190.

Programs

Maple

N:= 14: # to get all terms < 3^N
Res:= 2:
digrev:=proc(n) local L;
  L:= convert(n,base,3);
  add(L[-i]*3^(i-1),i=1..nops(L))
end proc;
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, op(select(isprime,[seq](n*3^m + digrev(n), n=3^(m-1)..3^m-1)));
  else
    m:= (d-1)/2;
    Res:= Res, op(select(isprime,[seq](seq(n*3^(m+1)+y*3^m+digrev(n),
      y=0..2), n=3^(m-1)..3^m-1)));
  fi
od:
Res; # Robert Israel, Aug 19 2015

Mathematica

Do[s = RealDigits[n, 3][[1]]; If[PrimeQ[n], If[FromDigits[s] == FromDigits[Reverse[s]], Print[n]]], {n, 1, 8500}]
Select[Prime[Range[8300]], Reverse[x = IntegerDigits[#, 3]] == x &] (* Jayanta Basu, Jun 23 2013 *)

PARI

lista(nn) = forprime(p=2, nn, if ((d=digits(p,3)) && (Vecrev(d)==d), print1(p, ", "))); \\ Michel Marcus, Aug 19 2015