A199341 Primes having only {1, 3, 4} as digits.

3, 11, 13, 31, 41, 43, 113, 131, 311, 313, 331, 431, 433, 443, 1433, 3313, 3331, 3343, 3413, 3433, 4111, 4133, 4441, 11113, 11131, 11311, 11411, 11443, 13313, 13331, 13411, 13441, 14143, 14341, 14411, 14431, 31333, 33113, 33311, 33331, 33343, 33413, 34141, 34313

Offset: 1

Author

M. F. Hasler, Nov 05 2011

Keywords

• nonn
• base

Comments

A020451, A020452 and A020461 are subsequences. - Vincenzo Librandi, Jul 26 2015

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Andrew Granville, Missing digits, and good approximations, arXiv:2308.03126 [math.NT], 2023. See p. 4.

Crossrefs

Cf. A020449 - A020472, A199325 - A199329.

Cf. similar sequences listed in A199340.

Programs

Magma

[p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // Vincenzo Librandi, Jul 26 2015

Maple

Dmax:= 5: # to get all terms < 10^Dmax
Cd:= {1,3,4}:
C:= Cd:
for d from 2 to Dmax do
  Cd:= map(t -> (10*t+1,10*t+3,10*t+4),Cd);
  C:= C union Cd;
od:
sort(convert(select(isprime,C),list)); # Robert Israel, Jul 26 2015

Mathematica

Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* Vincenzo Librandi, Jul 26 2015 *)

PARI

a(n, list=0, L=[1, 3, 4], reqpal=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]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}