A020451 Primes that contain digits 1 and 3 only.

3, 11, 13, 31, 113, 131, 311, 313, 331, 3313, 3331, 11113, 11131, 11311, 13313, 13331, 31333, 33113, 33311, 33331, 113111, 113131, 131111, 131113, 131311, 311111, 313133, 313331, 313333, 331333, 333131, 333331, 1111333, 1131113, 1131131, 1131133, 1131331

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Links

• Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Crossrefs

Subsequence of A030096, A045429, and A032917.

Programs

Magma

[p: p in PrimesUpTo(1131331) | Set(Intseq(p)) subset [1,3]]; // Bruno Berselli, Jul 27 2012

Maple

N:= 8: # to get all a(n) with at most N digits
S:= {}:
for d from 1 to N do
  r:= (10^d-1)/9;
  S:= S union select(isprime,map(`+`,map(convert,combinat[powerset]
      ({seq(2*10^i,i=0..d-1)}),`+`),r));
od:
S; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(S,list)); # Robert Israel, May 04 2015

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{1,3},n],PrimeQ],{n,7}]] (* Vincenzo Librandi, Jul 27 2012 *)

Python

from sympy import primerange
def checkd(a, c):
    b =  set(int(i) for i in set(str(a)))
    return b.issubset(c)
for n in primerange(2, 2000000):
    if checkd(n, [1, 3]):
        print(n)
# Abhiram R Devesh, May 04 2015