A260044 Primes having only {0, 1, 3} as digits.

3, 11, 13, 31, 101, 103, 113, 131, 311, 313, 331, 1013, 1031, 1033, 1103, 1301, 1303, 3001, 3011, 3301, 3313, 3331, 10103, 10111, 10133, 10301, 10303, 10313, 10331, 10333, 11003, 11113, 11131, 11311, 13001, 13003, 13033, 13103, 13313, 13331, 30011, 30013, 30103, 30113, 30133, 30313, 31013, 31033, 31333, 33013

Offset: 1

Author

M. F. Hasler, Jul 25 2015

Keywords

• nonn
• base

Comments

A subsequence of A107715 and of A111488.

Number of terms < 10^n: 1, 4, 11, 22, 54, 118, 293, 691, 1837, 4871, 13321, 36042, 98325, 272237, 757080, .... - Robert G. Wilson v, Jul 26 2015

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index to entries for primes with digits in a given set

Crossrefs

Cf. A020449 - A020472, A036953, A260266 - A260271, A199325 - A199329, A061247, A199340 - A199349.

Programs

Magma

[p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [0, 1, 3]]; // Vincenzo Librandi, Jul 26 2015

Mathematica

Select[ FromDigits@# & /@ Tuples[{0, 1, 3}, 5], PrimeQ] (* Robert G. Wilson v, Jul 26 2015 *)
Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {0, 1, 3}]=={} &] (* Vincenzo Librandi, Jul 26 2015 *)

PARI

A260044={(n,show=0,L=[0,1,3])->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)))}