A199325 Primes having only {0, 1, 5} as digits.

5, 11, 101, 151, 1051, 1151, 1511, 5011, 5051, 5101, 5501, 10111, 10151, 10501, 11551, 15101, 15511, 15551, 50051, 50101, 50111, 50551, 51001, 51151, 51511, 51551, 55001, 55051, 55501, 55511, 100151, 100501, 100511, 101051, 101111, 101501, 110051, 110501, 115001, 115151, 150001, 150011, 150151, 150551

Offset: 1

Author

M. F. Hasler, Nov 05 2011

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index to entries about primes with digits in a given set

Crossrefs

Cf. A020449 - A020472, A199326 - A199329, A061247, A199340 - A199349.

Programs

Magma

[p: p in PrimesUpTo(160000) | Set(Intseq(p)) subset [0, 1, 5]]; // Vincenzo Librandi, Apr 22 2014

Maple

N:= 10000: # to get the first N terms
count:= 0:
allowed:= {0,1,5}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1],i=0..nallowed-1):
for d from 0 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[FromDigits/@Tuples[{0,1,5},6],PrimeQ] (* Harvey P. Dale, Jul 23 2021 *)

PARI

L=[0,1,5];for(d=1,6,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)&print1(t",")))  /* see A199327 for a function a(n) */