A138584 Palindromic primes using only digits 3 and 5.

3, 5, 353, 33533, 35353, 3353533, 3553553, 333535333, 335333533, 355353553, 355555553, 33335353333, 33553335533, 35533333553, 35553535553, 3335535355333, 3335555555333, 3353353533533, 3353355533533, 3355535355533, 3533355533353, 3533533353353

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..5382

Maple

revdigs:= proc(n) option remember;
    local b;
    if n < 10 then return n fi;
    b:= n mod 10;
    b*10^ilog10(n) + procname((n-b)/10);
end proc:
A:= {3, 5}:
B:= [0]:
for d from 2 to 20 do
  if d::even then
    B:= map(t -> (10*t+3, 10*t+5), B);
    A:= A union select(isprime, {seq(revdigs(b)+10^(d/2)*b, b=B)});
  else
    A:= A union select(isprime, {seq(seq(
         revdigs(b)+i*10^((d-1)/2)+10^((d+1)/2)*b, i = [3, 5]), b=B)});
  fi
od:
sort(convert(A, list)); # Robert Israel, Dec 17 2015

Prog

(Python)
from itertools import product
from sympy import isprime
A138584_list = []
for l in range(17):
    for d in product('35', repeat=l):
        s = ''.join(d)
        n = int(s+'3'+s[::-1])
        if isprime(n):
            A138584_list.append(n)
        n += 2*10**l
        if isprime(n):
            A138584_list.append(n) # Chai Wah Wu, Dec 17 2015

Crossrefs

Cf. A020462.

Sequence in context: A280035 A087670 A271390 * A277995 A354245 A247699

Adjacent sequences: A138581 A138582 A138583 * A138585 A138586 A138587

Keyword

nonn,base

Author

Paul Curtz, May 13 2008

Extensions

More terms from Arkadiusz Wesolowski, Dec 31 2011

Status

approved