A061247 Primes having only {0, 1, 8} as digits.

11, 101, 181, 811, 881, 1181, 1801, 1811, 8011, 8081, 8101, 8111, 10111, 10181, 11801, 18181, 80111, 81001, 81101, 81181, 88001, 88801, 88811, 100801, 100811, 101081, 101111, 108011, 108881, 110881, 118081, 118801, 180001, 180181, 180811

Offset: 1

Author

Amarnath Murthy, Apr 23 2001

Keywords

• nonn
• base

Comments

The intersection with A007500 is listed in A199328. - M. F. Hasler, Nov 05 2011

Examples

			a(6) = 1801, 1801 is a prime and consists of only 1, 8 and 0.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..17482

Crossrefs

Cf. A061246, A020449-A020472, A199325-A199329.

Programs

Magma

[NthPrime(n): n in [1..2*10^4] | forall{d: d in Intseq(NthPrime(n)) | d in [0, 1, 8]}]; // Vincenzo Librandi, May 15 2019

Maple

N:= 1000: # to get the first N entries
count:= 0:
allowed:= {0,1,8}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1],i=0..nallowed-1);
for d from 1 while count < N do
  for x1 from 1 to nallowed-1 while count < N do
    for t from 0 to nallowed^d-1  while count < N do
      L:= subs(subst,convert(x1*nallowed^d+t,base,nallowed));
      X:= add(L[i]*10^(i-1),i=1..d+1);
      if isprime(X) then
          count:= count+1;
          A[count]:= X;
      fi
od od od:
seq(A[n],n=1..N); # Robert Israel, Apr 20 2014

Mathematica

Select[Prime[Range[50000]],Length[Union[{0,1,8},IntegerDigits[ # ]]] == 3&] (* Stefan Steinerberger, Jun 10 2007 *)
Select[FromDigits/@Tuples[{0,1,8},6],PrimeQ] (* Harvey P. Dale, Jan 12 2016 *)

PARI

a(n=50, L=[0, 1, 8], show=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1 && !L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u) || next; show && print1(t", "); n-- || return(t)))} \\ M. F. Hasler, Nov 05 2011

Extensions

Corrected and extended by Stefan Steinerberger, Jun 10 2007