cp's OEIS Frontend

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

%I A199341 #20 Jul 15 2025 10:51:44
%S A199341 3,11,13,31,41,43,113,131,311,313,331,431,433,443,1433,3313,3331,3343,
%T A199341 3413,3433,4111,4133,4441,11113,11131,11311,11411,11443,13313,13331,
%U A199341 13411,13441,14143,14341,14411,14431,31333,33113,33311,33331,33343,33413,34141,34313
%N A199341 Primes having only {1, 3, 4} as digits.
%C A199341 A020451, A020452 and A020461 are subsequences. - _Vincenzo Librandi_, Jul 26 2015
%H A199341 Robert Israel, <a href="/A199341/b199341.txt">Table of n, a(n) for n = 1..10000</a>
%H A199341 Andrew Granville, <a href="https://arxiv.org/abs/2308.03126">Missing digits, and good approximations</a>, arXiv:2308.03126 [math.NT], 2023. See p. 4.
%p A199341 Dmax:= 5: # to get all terms < 10^Dmax
%p A199341 Cd:= {1,3,4}:
%p A199341 C:= Cd:
%p A199341 for d from 2 to Dmax do
%p A199341   Cd:= map(t -> (10*t+1,10*t+3,10*t+4),Cd);
%p A199341   C:= C union Cd;
%p A199341 od:
%p A199341 sort(convert(select(isprime,C),list)); # _Robert Israel_, Jul 26 2015
%t A199341 Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* _Vincenzo Librandi_, Jul 26 2015 *)
%o A199341 (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)))}
%o A199341 (Magma) [p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // _Vincenzo Librandi_, Jul 26 2015
%Y A199341 Cf. A020449 - A020472, A199325 - A199329.
%Y A199341 Cf. similar sequences listed in A199340.
%K A199341 nonn,base
%O A199341 1,1
%A A199341 _M. F. Hasler_, Nov 05 2011